quiz 9 hypothesis testing for two populations

8/10/2019 Quiz 9 Hypothesis Testing for Two Populations

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Quiz 9 Hypothesis testing for two populations

1. Two samples of sizes 25 and 35 are independently drawn from two normal

populations, where the unknown arian!es are assumed to "e e#ual. The num"er of

degrees of freedom for the e#ual$arian!es t$test statisti! is%

&a. 5'". ()

!. (2

d. 5*

e. ('

2. Two samples of sizes 2* and 35 are independently drawn from two normal



a. 5'

&". ()

!. (2d. 5*

e. ('

3. Two samples of sizes 25 and 39 are independently drawn from two normal



a. 5'

". ()

&!. (2

d. 5*

e. ('

+. Two samples of sizes 2+ and 35 are independently drawn from two normal



a. 5'

". ()

!. (2

&d. 5*

e. ('

5. Two samples of sizes 25 and +5 are independently drawn from two normal



a. 5'

". ()

!. (2

d. 5*

&e. ('

(. hen the ne!essary !onditions are met, a two$tail test is !ondu!ted to test the

differen!e "etween two population means. The statisti!al software in use only


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proides one tail p$alues as part of its output. -ien a one$tail p$alue of ).)3(,

what would a two$tail p$alue for the same test "e

a. ).)1'

". ).))9

&!. ).)*2

d. ).9(+e. ).3()

*. hi!h of the following statements is !orre!t

&a. independent samples are those for whi!h the sele!tion pro!ess for one sample is

not related to the sele!tion pro!ess for the other sample

". !omparing the means from two independent samples re#uires !omparing the alue

of the !al!ulated test statisti! with the p$alue in order to de!ide whether the null

hypothesis should "e re/e!ted or not

!. an e0ample of dependent samples o!!urs when su"/e!ts are randomly assigned to

the e0perimental and !ontrol groups of an e0periment

d. a typi!al e0ample of independent samples o!!urs with "efore and aftermeasurements for the same indiiduals or test units

e. a spe!ial hypothesis test, "ased on the t$distri"ution, !an "e applied to test the null

hypothesis that the population arian!es for two independent samples are e#ual

'. hi!h of the following statements is !orre!t

a. the pooled$arian!es t$test is used wheneer the population standard deiations !an

"e assumed to "e e#ual, regardless of the sample size

". the une#ual$arian!es t$test is used wheneer the population standard deiations are

unknown and !annot assumed to "e e#ual

!. the z$test !an "e used as a !lose appro0imation to the une#ual$arian!es t$test when

the population standard deiation are not assumed to "e e#ual "ut sample sizes are

large typi!ally greater than 3)

&d. all of the a"oe statements are true

e. none of the a"oe statements are true

9. ssuming that samples are drawn from normal distri"utions, whi!h of the following

statement is false

a. The pooled$arian!es t$test is used wheneer the population standard deiations are

assumed to "e e#ual

". The une#ual$arian!es t$test is used wheneer the population standard deiations

are unknown and !annot "e assumed to "e e#ual!. The z$test !an "e used as a !lose appro0imation to the une#ual$arian!es t$test

when the population standard deiations are not assumed to "e e#ual, "ut samples are

large typi!ally greater than 3)

&d. The null hypothesis in the 4$test for !omparing two population arian!es states

that the sample arian!es are e#ual

e. The null hypothesis for a hypothesis test !omparing two population means states

that the population arian!es are e#ual

1). Two independent samples from populations that are normally distri"uted produ!ed

the following statisti!s% for sample 1 the sample size was 5), the sample mean was

3+.2 and the sample standard deiation was 12.(. 4or sample 2, the sample size was+2, the sample mean was +9.1 and the sample standard deiation was 19.+. ssume


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that population arian!es are e#ual. -ien a signifi!an!e leel of 5, at what

appro0imate alue of t should you re/e!t the null hypothesis that states that the two

population means are e#ual, in faour of the two sided alternatie

&a. 61.9'*

". 61.99)

!. 61.99+d. 62.)21

e. 62.))9

11. Two independent samples from populations that are normally distri"uted produ!ed

the following statisti!s% for sample 1 the sample size was 5), the sample mean was

3+.2 and the sample standard deiation was 12.(. 4or sample 2, the sample size was

32, the sample mean was +9.1 and the sample standard deiation was 19.+. ssume




a. 61.9'*&". 61.99)

!. 61.99+

d. 62.)21

e. 62.))9


the following statisti!s% for sample 1 the sample size was +), the sample mean was


32, the sample mean was +9.1 and the sample standard deiation was 19.+. ssume




a. 61.9'*

". 61.99)

&!. 61.99+

d. 62.)21

e. 62.))9


the following statisti!s% for sample 1 the sample size was 19, the sample mean was

3+.2 and the sample standard deiation was 12.(. 4or sample 2, the sample size was23, the sample mean was +9.1 and the sample standard deiation was 19.+. ssume




a. 61.9'*

". 61.99)

!. 61.99+

&d. 62.)21

e. 62.))9

1+. Two independent samples from populations that are normally distri"uted produ!edthe following statisti!s% for sample 1 the sample size was 25, the sample mean was


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2*, the sample mean was +9.1 and the sample standard deiation was 19.+. ssume




a. 61.9'*". 61.99)

!. 61.99+

d. 62.)21

&e. 62.))9

15. hi!h of the following statements regarding the 4 distri"ution is false

a. The 4 distri"ution is skewed to the right

". The 4 distri"ution has two sets of degrees of freedom

&!. The 4 distri"ution always has a mean of 1

d. The 4 distri"ution is used to test the null hypothesis that the population arian!es

are e#uale. The 4 distri"ution is an all positie distri"ution

1(. hi!h of the following statements !orre!tly des!ri"es a differen!e "etween the 4

and t distri"utions

a. The 4 distri"ution is dis!rete, the t distri"ution is !ontinuous

". The t distri"ution is alid only for positie num"ers, the 4 for all real alues

!. The 4 distri"ution is symmetri!al, the t distri"ution is skewed to the right

&d. The 4 distri"ution is alid only for positie num"ers, the t for all real alues

e. The 4 distri"ution is skewed to the left, the t distri"ution is symmetri!al

1*. The owner of 7un 8 un Ham"urgers wishes to !ompare the sales per day at two

different lo!ations. The mean num"er of ham"urgers sold for 1) randomly sele!ted

days at :orthside was '3.55 with a population standard deiation of 1).5). 4or a

randomly sele!ted 12 days at ;outhside, the mean num"er of ham"urgers sold was

*3.') with a population standard deiation of 1+.25. e wish to test whether there is

a differen!e in the mean num"er of ham"urgers sold at the two lo!ations using a 5

signifi!an!e leel. hat is the alue of the test statisti! in this !ase

&a. 1.'+

". ).2+

!. 2.(5

d. 1.*1e. 2.2)

1'. The owner of 7un 8 un Ham"urgers wishes to !ompare the sales per day at two


days at :orthside was *5.)( with a population standard deiation of 1).5). 4or a





a. 1.'+

&". ).2+!. 2.(5


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d. 1.*1

e. 2.2)

19. The owner of 7un 8 un Ham"urgers wishes to !ompare the sales per day at two


days at :orthside was '3.55 with a population standard deiation of 1).5). 4or arandomly sele!ted 12 days at ;outhside, the mean num"er of ham"urgers sold was

(9.5+ with a population standard deiation of 1+.25. e wish to test whether there is



a. 1.'+

". ).2+

&!. 2.(5

d. 1.*1

e. 2.2)

2). The owner of 7un 8 un Ham"urgers wishes to !ompare the sales per day at twodifferent lo!ations. The mean num"er of ham"urgers sold for 1) randomly sele!ted

days at :orthside was '3.55 with a population standard deiation of 12.+5. 4or a





a. 1.'+

". ).2+

!. 2.(5

&d. 1.*1

e. 2.2)



days at :orthside was '3.55 with a population standard deiation of 1).5). 4or a


*3.') with a population standard deiation of 1).2). e wish to test whether there is



a. 1.'+

". ).2+!. 2.(5

d. 1.*1

&e. 2.2)



days at :orthside was '3.55 with a population standard deiation of 12.+5. 4or a




signifi!an!e leel. hat is the !orre!t !on!lusion for this hypothesis test


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a.


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&". $2.1(

!. $).'(

d. $1.+)

e. $1.('

2(. resear!her randomly sampled 3) graduates of an =7 program and re!ordeddata !on!erning their starting salaries. The sample !omprised of 1' women whose

aerage starting salary is +' ))), and 12 men whose aerage starting salary is 52

))). >t is known that the population standard deiations of starting salaries for women

and men are 11 5)) and 13 ))) respe!tiely. The resear!her was attempting to

show that female =7 graduates hae signifi!antly lower aerage starting salaries

than male =7 graduates. hat is the alue of the test statisti! in this !ase

a. $1.51

". $2.1(

&!. $).'(

d. $1.+)

e. $1.('

2*. resear!her randomly sampled 3) graduates of an =7 program and re!orded

data !on!erning their starting salaries. The sample !omprised of 1' women whose



and men are 1+ ))) and 13 ))) respe!tiely. The resear!her was attempting to


than male =7 graduates. hat is the alue of the test statisti! in this !ase

a. $1.51

". $2.1(

!. $).'(

&d. $1.+)

e. $1.('

2'. resear!her randomly sampled 3) graduates of an =7 program and re!orded






than male =7 graduates. hat is the alue of the test statisti! in this !asea. $1.51

". $2.1(

!. $).'(

d. $1.+)

&e. $1.('

29. resear!her randomly sampled 3) graduates of an =7 program and re!orded






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than male =7 graduates. hat is the p$alue of the test in this !ase

&a. ).)(55

". ).)15+

!. ).19+9

d. ).)')'e. ).)+(5

3). resear!her randomly sampled 3) graduates of an =7 program and re!orded


aerage starting salary is +5 ))), and 12 men whose aerage starting salary is 55





a. ).)(55

&". ).)15+!. ).19+9

d. ).)')'

e. ).)+(5








a. ).)(55

". ).)15+

&!. ).19+9

d. ).)')'

e. ).)+(5




))). >t is known that the population standard deiations of starting salaries for womenand men are 1+ ))) and 13 ))) respe!tiely. The resear!her was attempting to



a. ).)(55

". ).)15+

!. ).19+9

&d. ).)')'

e. ).)+(5


data !on!erning their starting salaries. The sample !omprised of 1' women whoseaerage starting salary is +' ))), and 12 men whose aerage starting salary is 55


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a. ).)(55

". ).)15+!. ).19+9

d. ).)')'

&e. ).)+(5

3+. >t is known that the population arian!es of final e0am marks for first year

statisti!s students at a parti!ular ;outh fri!an uniersity are +5.3 for female students

and 52.1 for male students. ;amples of 2* female and 31 male first year statisti!s

students from the uniersity are sele!ted and the sample mean e0am marks are

!al!ulated. 4or females, the sample mean mark is 5*.3 and for males the sample

mean mark is 55.+. >f we wish to test whether females hae, on aerage, higher

e0am marks than males, what would the test statisti! alue of the hypothesis test inthis !ase "e

&a. 1.)+

". 1.5'

!. ).+9

d. $1.15

e. $1.(9

35. >t is known that the population arian!es of final e0am marks for first year




!al!ulated. 4or females, the sample mean mark is 5'.3 and for males the sample


e0am marks than males, what would the test statisti! alue of the hypothesis test in

this !ase "e

a. 1.)+

&". 1.5'

!. ).+9

d. $1.15

e. $1.(9

3(. >t is known that the population arian!es of final e0am marks for first year





mean mark is 5(.+. >f we wish to test whether females hae, on aerage, higher


this !ase "e

a. 1.)+

". 1.5'

&!. ).+9d. $1.15


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e. $1.(9

3*. >t is known that the population arian!es of final e0am marks for first year



students from the uniersity are sele!ted and the sample mean e0am marks are!al!ulated. 4or females, the sample mean mark is 5*.3 and for males the sample



this !ase "e

a. 1.)+

". 1.5'

!. ).+9

&d. $1.15

e. $1.(9

3'. >t is known that the population arian!es of final e0am marks for first yearstatisti!s students at a parti!ular ;outh fri!an uniersity are +5.3 for female students



!al!ulated. 4or females, the sample mean mark is 52.3 and for males the sample



this !ase "e

a. 1.)+

". 1.5'

!. ).+9

d. $1.15

&e. $1.(9

39. >t is known that the population arian!es of final e0am marks for first year






e0am marks than males, what would the p$alue of the hypothesis test in this !ase "e

&a. ).15". ).)(

!. ).31

d. ).'*

e. ).95

+). >t is known that the population arian!es of final e0am marks for first year




!al!ulated. 4or females, the sample mean mark is 5'.3 and for males the sample

mean mark is 55.+. >f we wish to test whether females hae, on aerage, highere0am marks than males, what would the p$alue of the hypothesis test in this !ase "e


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a. ).15

&". ).)(

!. ).31

d. ).'*

e. ).95

+1. >t is known that the population arian!es of final e0am marks for first year





mean mark is 5(.+. >f we wish to test whether females hae, on aerage, higher


a. ).15

". ).)(

&!. ).31

d. ).'*e. ).95








a. ).15

". ).)(

!. ).31

&d. ).'*

e. ).95





!al!ulated. 4or females, the sample mean mark is 52.3 and for males the sample

mean mark is 55.+. >f we wish to test whether females hae, on aerage, highere0am marks than males, what would the p$alue of the hypothesis test in this !ase "e

a. ).15

". ).)(

!. ).31

d. ).'*

&e. ).95

++. random sample of 1) male and 12 female students? !lass test 1 marks were

re!orded. The sample mean mark for the males was 5(.2 and the standard

deiation was 12.'. The sample mean mark for the females was 5+.5 with a

standard deiation of 11.*. hat would "e the alue of the pooled arian!e&a. 1+9.)2


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". 152.++

!. 139.)*

d. 1+*.92

e. 121.19

+5. random sample of 1( male and 12 female students? !lass test 1 marks werere!orded. The sample mean mark for the males was 5(.2 and the standard


standard deiation of 11.*. hat would "e the alue of the pooled arian!e

a. 1+9.)2

&". 152.++

!. 139.)*

d. 1+*.92

e. 121.19

+(. random sample of 1) male and 12 female students? !lass test 1 marks were

re!orded. The sample mean mark for the males was 5(.2 and the standarddeiation was 12.'. The sample mean mark for the females was 5+.5 with a

standard deiation of 1).9. hat would "e the alue of the pooled arian!e

a. 1+9.)2

". 152.++

&!. 139.)*

d. 1+*.92

e. 121.19

+*. random sample of 1) male and 1+ female students? !lass test 1 marks were



standard deiation of 11.*. hat would "e the alue of the pooled arian!e

a. 1+9.)2

". 152.++

!. 139.)*

&d. 1+*.92

e. 121.19

+'. random sample of 1) male and 12 female students? !lass test 1 marks were


deiation was 1).1. The sample mean mark for the females was 5+.5 with astandard deiation of 11.*. hat would "e the alue of the pooled arian!e

a. 1+9.)2

". 152.++

!. 139.)*

d. 1+*.92

&e. 121.19

+9. random sample of 1) male and 12 female students? !lass test 1 marks were



standard deiation of 11.*. e wish to test whether the aerage marks for test 1 for


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males and females differ, at the 5 signifi!an!e leel. >f we assume e#ual underlying

population arian!es, what is the alue of the test statisti!

&a. ).33

". ).3(

!. ).(3

d. 1.39e. 2.12

5). random sample of 1( male and 12 female students? !lass test 1 marks were



standard deiation of 11.*. e wish to test whether the aerage marks for test 1 for



a. ).33

&". ).3(

!. ).(3d. 1.39

e. 2.12

51. random sample of 1) male and 12 female students? !lass test 1 marks were

re!orded. The sample mean mark for the males was 5'.) and the standard

deiation was 15.1. The sample mean mark for the females was 5+.5 with a

standard deiation of 1).9. e wish to test whether the aerage marks for test 1 for



a. ).33

". ).3(

&!. ).(3

d. 1.39

e. 2.12

52. random sample of 1) male and 1+ female students? !lass test 1 marks were

re!orded. The sample mean mark for the males was 59 and the standard deiation

was 12.'. The sample mean mark for the females was 52 with a standard

deiation of 11.*. e wish to test whether the aerage marks for test 1 for males

and females differ, at the 5 signifi!an!e leel. >f we assume e#ual underlying

population arian!es, what is the alue of the test statisti!a. ).33

". ).3(

!. ).(3

&d. 1.39

e. 2.12

53. random sample of 1) male and 12 female students? !lass test 1 marks were

re!orded. The sample mean mark for the males was (1 and the standard deiation

was 1).1. The sample mean mark for the females was 51 with a standard

deiation of 11.*. e wish to test whether the aerage marks for test 1 for males

and females differ, at the 5 signifi!an!e leel. >f we assume e#ual underlyingpopulation arian!es, what is the alue of the test statisti!


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a. ).33

". ).3(

!. ).(3

d. 1.39

&e. 2.12

5+. new -rade 9 maths !urri!ulum is to "e tested. num"er of students in a -rade

9 maths !ourse at a parti!ular high s!hool were randomly diided into two groups.

The e0perimental group re!eied tea!hing a!!ording to the new !urri!ulum while the

!ontrol group did not. ll the students were gien a test of !omputational skill out of

a total of 5 points after the !ourse and the results were as follows% for the

e0perimental group, the sample size was 2', the sample mean was 1.19 and the

sample arian!e was *+. 4or the !ontrol group, the sample size was 31, the sample

mean was 3.5+ and the sample arian!e was '). e wish to test at the 5 leel of

signifi!an!e whether there is any differen!e in the mean test s!ores. e assume that

the underlying population arian!es are e#ual. hat is the alue of the test statisti!

for this hypothesis test&a. $1.)3

". ).++

!. $).')

d. $).((

e. ).13

55. new -rade 9 maths !urri!ulum is to "e tested. num"er of students in a -rade





e0perimental group, the sample size was 2', the sample mean was +.52 and the

sample arian!e was (+. 4or the !ontrol group, the sample size was 31, the sample




for this hypothesis test

a. $1.)3

&". ).++

!. $).')

d. $).((e. ).13

5(. new -rade 9 maths !urri!ulum is to "e tested. num"er of students in a -rade







mean was 2.99 and the sample arian!e was *5. e wish to test at the 5 leel of



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a. $1.)3

". ).++

&!. $).')

d. $).((e. ).13

5*. new -rade 9 maths !urri!ulum is to "e tested. num"er of students in a -rade






sample arian!e was '5. 4or the !ontrol group, the sample size was 31, the sample


signifi!an!e whether there is any differen!e in the mean test s!ores. e assume thatthe underlying population arian!es are e#ual. hat is the alue of the test statisti!


a. $1.)3

". ).++

!. $).')

&d. $).((

e. ).13

5'. new -rade 9 maths !urri!ulum is to "e tested. num"er of students in a -rade







mean was ).'9 and the sample arian!e was '2. e wish to test at the 5 leel of




a. $1.)3

". ).++!. $).')

d. $).((

&e. ).13

59. new -rade 9 maths !urri!ulum is to "e tested. num"er of students in a -rade






sample arian!e was *+. 4or the !ontrol group, the sample size was 31, the samplemean was 3.5+ and the sample arian!e was '). e wish to test at the 5 leel of


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the underlying population arian!es are e#ual. hat is the alue of the pooled

arian!e for this test

&a. **.1(

". *2.+2

!. *+.53d. '2.3*

e. *'.21

(). new -rade 9 maths !urri!ulum is to "e tested. num"er of students in a -rade





e0perimental group, the sample size was 2', the sample mean was +.52 and the

sample arian!e was (+. 4or the !ontrol group, the sample size was 31, the sample

mean was 3.5+ and the sample arian!e was '). e wish to test at the 5 leel ofsignifi!an!e whether there is any differen!e in the mean test s!ores. e assume that



a. **.1(

&". *2.+2

!. *+.53

d. '2.3*

e. *'.21

(1. new -rade 9 maths !urri!ulum is to "e tested. num"er of students in a -rade







mean was 2.99 and the sample arian!e was *5. e wish to test at the 5 leel of




a. **.1(". *2.+2

&!. *+.53

d. '2.3*

e. *'.21






e0perimental group, the sample size was 2', the sample mean was 1.99 and thesample arian!e was '5. 4or the !ontrol group, the sample size was 31, the sample


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a. **.1(

". *2.+2!. *+.53

&d. '2.3*

e. *'.21







sample arian!e was *+. 4or the !ontrol group, the sample size was 31, the samplemean was ).'9 and the sample arian!e was '2. e wish to test at the 5 leel of




a. **.1(

". *2.+2

!. *+.53

d. '2.3*

&e. *'.21

(+. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at

night does not result in saing of ele!tri!ity. >n order to test this !laim a newspaper

reporter o"tains the !o$operation of 1( house owners with similar houses and salaries.

@ight of the sele!ted owners swit!h their !ylinders off at night. The !onsumption of

ele!tri!ity in ea!h house oer a period of 3) days is measuredA the units are kh

kilowatt$hours. 4or households that swit!hed off their hot water !ylinders, aerage

!onsumption oer the 3) days was (')kh with a arian!e of +5)kh2. 4or those

that did not swit!h off their hot water !ylinders, aerage ele!tri!ity !onsumption was

*))kh with a arian!e of 3))kh2. >f we assume that the underlying population

arian!es are not e#ual and we wish to test whether the mean ele!tri!ity !onsumption

for those households that turned off their hot water !ylinders was lower than for thosethat did not, what would "e the alue of the appropriate test statisti!

&a. $2.)*

". $1.55

!. $1.)3

d. $2.5'

e. $).52

(5. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at



@ight of the sele!ted owners swit!h their !ylinders off at night. The !onsumption ofele!tri!ity in ea!h house oer a period of 3) days is measuredA the units are kh


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!onsumption oer the 3) days was ('5kh with a arian!e of +5)kh2. 4or those




for those households that turned off their hot water !ylinders was lower than for thosethat did not, what would "e the alue of the appropriate test statisti!

a. $2.)*

&". $1.55

!. $1.)3

d. $2.5'

e. $).52

((. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at



@ight of the sele!ted owners swit!h their !ylinders off at night. The !onsumption ofele!tri!ity in ea!h house oer a period of 3) days is measuredA the units are kh


!onsumption oer the 3) days was (9)kh with a arian!e of +5)kh2. 4or those




for those households that turned off their hot water !ylinders was lower than for those

that did not, what would "e the alue of the appropriate test statisti!

a. $2.)*

". $1.55

&!. $1.)3

d. $2.5'

e. $).52

(*. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at






!onsumption oer the 3) days was (')kh with a arian!e of +5)kh2

. 4or thosethat did not swit!h off their hot water !ylinders, aerage ele!tri!ity !onsumption was

*)5kh with a arian!e of 3))kh2. >f we assume that the underlying population




a. $2.)*

". $1.55

!. $1.)3

&d. $2.5'

e. $).52


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('. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at





kilowatt$hours. 4or households that swit!hed off their hot water !ylinders, aerage!onsumption oer the 3) days was (95kh with a arian!e of +5)kh2. 4or those






a. $2.)*

". $1.55

!. $1.)3

d. $2.5'

&e. $).52

(9. !omparison of the pri!e$earnings BC@ ratio for the top and "ottom 1))

!ompanies on the D;@ is "eing prepared. finan!ial adisor randomly sampled ea!h

group to determine whether there is any differen!e in BC@ ratios of the two groups of

!ompanies. ssume une#ual population arian!es "ut that the populations are

normally distri"uted. 4or ( top 1)) !ompanies the aerage BC@ ratio was 1'.'3 with a

sample arian!e of 12'.1*. 4or ' "ottom 1)) !ompanies the aerage BC@ ratio was

1).(* with a sample arian!e of 125.15. The test is !ondu!ted at the 5 leel of

signifi!an!e. hat would "e the alue of the test statisti! for the hypothesis test in this

!ase

&a. 1.3+

". ).*+

!. 1.(*

d. 1.*)

e. 2.25

*). !omparison of the pri!e$earnings BC@ ratio for the top and "ottom 1))




normally distri"uted. 4or ( top 1)) !ompanies the aerage BC@ ratio was 15.15 with asample arian!e of 12'.1*. 4or ' "ottom 1)) !ompanies the aerage BC@ ratio was



!ase

a. 1.3+

&". ).*+

!. 1.(*

d. 1.*)

e. 2.25

*1. !omparison of the pri!e$earnings BC@ ratio for the top and "ottom 1))!ompanies on the D;@ is "eing prepared. finan!ial adisor randomly sampled ea!h


20/29





'.(* with a sample arian!e of 125.15. The test is !ondu!ted at the 5 leel of

signifi!an!e. hat would "e the alue of the test statisti! for the hypothesis test in this!ase

a. 1.3+

". ).*+

&!. 1.(*

d. 1.*)

e. 2.25

*2. !omparison of the pri!e$earnings BC@ ratio for the top and "ottom 1))



!ompanies. ssume une#ual population arian!es "ut that the populations arenormally distri"uted. 4or ( top 1)) !ompanies the aerage BC@ ratio was 21.)3 with a




!ase

a. 1.3+

". ).*+

!. 1.(*

&d. 1.*)

e. 2.25

*3. !omparison of the pri!e$earnings BC@ ratio for the top and "ottom 1))






5.1+ with a sample arian!e of 125.15. The test is !ondu!ted at the 5 leel of


!ase

a. 1.3+". ).*+

!. 1.(*

d. 1.*)

&e. 2.25

*+. so!iologist wants to test if there is any differen!e "etween the mean in!ome of

farm workers in two different areas. >n area a random sample of +1 workers yielded

a mean in!ome of 155(1 with a standard deiation of 9)1). >n area 7 a random

sample of 9 workers yielded a mean in!ome of 15)*' and a standard deiation of

5(2+. >f we assume that the population arian!es are not e#ual, what would "e the

alue of the test statisti! for the hypothesis test in this !ase&a. ).21


21/29

". 1.25

!. ).(*

d. 2.53

e. 1.95

*5. so!iologist wants to test if there is any differen!e "etween the mean in!ome offarm workers in two different areas. >n area a random sample of +1 workers yielded

a mean in!ome of 1'))) with a standard deiation of 9)1). >n area 7 a random



alue of the test statisti! for the hypothesis test in this !ase

a. ).21

&". 1.25

!. ).(*

d. 2.53

e. 1.95

*(. so!iologist wants to test if there is any differen!e "etween the mean in!ome of



sample of 9 workers yielded a mean in!ome of 1+))) and a standard deiation of



a. ).21

". 1.25

&!. ).(*

d. 2.53

e. 1.95

**. so!iologist wants to test if there is any differen!e "etween the mean in!ome of


a mean in!ome of 21))) with a standard deiation of 9)1). >n area 7 a random




a. ).21

". 1.25

!. ).(*&d. 2.53

e. 1.95

*'. so!iologist wants to test if there is any differen!e "etween the mean in!ome of



sample of 9 workers yielded a mean in!ome of 11))) and a standard deiation of



a. ).21

". 1.25!. ).(*


22/29

d. 2.53

&e. 1.95

*9. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at


reporter o"tains the !o$operation of 1( house owners with similar houses and salaries.@ight of the sele!ted owners swit!h their !ylinders off at night. The !onsumption of





*))kh with a arian!e of 3))kh2. >f we wish to test the assumption of e#ual

population arian!es at the 5 leel of signifi!an!e, what is the alue of the test

statisti!

&a. 1.5)

". 1.+2

!. 1.29d. 1.33

e. 1.55

'). The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at






!onsumption oer the 3) days was (')kh with a arian!e of +25kh2. 4or those




statisti!

a. 1.5)

&". 1.+2

!. 1.29

d. 1.33

e. 1.55

'1. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder atnight does not result in saing of ele!tri!ity. >n order to test this !laim a newspaper







*))kh with a arian!e of 35)kh2. >f we wish to test the assumption of e#ual


statisti!

a. 1.5)". 1.+2


23/29

&!. 1.29

d. 1.33

e. 1.55

'2. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at

night does not result in saing of ele!tri!ity. >n order to test this !laim a newspaperreporter o"tains the !o$operation of 1( house owners with similar houses and salaries.




!onsumption oer the 3) days was (')kh with a arian!e of +))kh2. 4or those




statisti!

a. 1.5)

". 1.+2!. 1.29

&d. 1.33

e. 1.55

'3. The national ele!tri!ity supplier !laims that swit!hing off the hot water !ylinder at








*))kh with a arian!e of 29)kh2. >f we wish to test the assumption of e#ual


statisti!

a. 1.5)

". 1.+2

!. 1.29

d. 1.33

&e. 1.55

'+. >n a test to determine whether two population arian!es are e#ual, the !al!ulated

test statisti! alue e#ualled +.12. The numerator degrees of freedom were 2 and the

denominator degrees of freedom were 13. The test was one$sided and !ondu!ted at

the 5 leel of signifi!an!e. hat was the !orre!t !on!lusion to the test in this !ase

a. do not re/e!t the null hypothesis at the 5 leel of signifi!an!e and !on!lude that

the one arian!e is signifi!antly larger than the other

". re/e!t the null hypothesis at the 5 leel of signifi!an!e and !on!lude that there is

no differen!e "etween the two population arian!es

!. do not re/e!t the null hypothesis at the 5 leel of signifi!an!e and !on!lude that

there is no differen!e "etween the two population arian!es

&d. re/e!t the null hypothesis at the 5 leel of signifi!an!e and !on!lude that the onearian!e is signifi!antly larger than the other


24/29

e. there is not enough information presented here to "e a"le to make a !on!lusion

'5. >n a test to determine whether two population arian!es are e#ual, the !al!ulated

test statisti! alue e#ualled 3.12. The numerator degrees of freedom were 2 and the

denominator degrees of freedom were 13. The test was one$sided and !ondu!ted at

the 5 leel of signifi!an!e. hat was the !orre!t !on!lusion to the test in this !asea. do not re/e!t the null hypothesis at the 5 leel of signifi!an!e and !on!lude that

the one arian!e is signifi!antly larger than the other

". re/e!t the null hypothesis at the 5 leel of signifi!an!e and !on!lude that there is

no differen!e "etween the two population arian!es

&!. do not re/e!t the null hypothesis at the 5 leel of signifi!an!e and !on!lude that

there is no differen!e "etween the two population arian!es

d. re/e!t the null hypothesis at the 5 leel of signifi!an!e and !on!lude that the one

arian!e is signifi!antly larger than the other

e. there is not enough information presented here to "e a"le to make a !on!lusion

'(. Two samples are drawn, one ea!h from an independent normally distri"utedpopulation. The sample size for sample 1 is 1(, while the sample arian!e is +*.3.

4or sample 2, the sample size is 13, while the sample arian!e is 3(.+. e wish to

test whether the population arian!e of population 1 is greater than the population

arian!e of population 2. hat is the alue of the test statisti! in this !ase

&a. 1.3)

". 1.3+

!. 1.5)

d. 1.+1

e. 1.)2

'*. Two samples are drawn, one ea!h from an independent normally distri"uted

population. The sample size for sample 1 is 1(, while the sample arian!e is +'.9.




a. 1.3)

&". 1.3+

!. 1.5)

d. 1.+1

e. 1.)2

''. Two samples are drawn, one ea!h from an independent normally distri"uted

population. The sample size for sample 1 is 1(, while the sample arian!e is +*.3.

4or sample 2, the sample size is 13, while the sample arian!e is 31.(. e wish to



a. 1.3)

". 1.3+

&!. 1.5)

d. 1.+1

e. 1.)2


25/29

'9. Two samples are drawn, one ea!h from an independent normally distri"uted

population. The sample size for sample 1 is 1(, while the sample arian!e is 51.2.




a. 1.3)". 1.3+

!. 1.5)

&d. 1.+1

e. 1.)2

9). Two samples are drawn, one ea!h from an independent normally distri"uted


4or sample 2, the sample size is 13, while the sample arian!e is +(.5. e wish to



a. 1.3)". 1.3+

!. 1.5)

d. 1.+1

&e. 1.)2

91. Two samples are drawn, one ea!h from an independent normally distri"uted




arian!e of population 2. hat is the !riti!al alue of the test in this !ase, if we test at

the 5 leel of signifi!an!e

&a. 2.(2

". 3.22

!. 3.)*

d. 2.*5

e. +.39


population. The sample size for sample 1 is 1(, while the sample arian!e is +'.9.

4or sample 2, the sample size is 9, while the sample arian!e is 3(.+. e wish to test

whether the population arian!e of population 1 is greater than the populationarian!e of population 2. hat is the !riti!al alue of the test in this !ase, if we test at


a. 2.(2

&". 3.22

!. 3.)*

d. 2.*5

e. +.39


population. The sample size for sample 1 is 13, while the sample arian!e is +*.3.

4or sample 2, the sample size is 1), while the sample arian!e is 31.(. e wish totest whether the population arian!e of population 1 is greater than the population


26/29



a. 2.(2

". 3.22

&!. 3.)*

d. 2.*5e. +.39

9+. Two samples are drawn, one ea!h from an independent normally distri"uted

population. The sample size for sample 1 is 11, while the sample arian!e is 51.2.





a. 2.(2

". 3.22

!. 3.)*&d. 2.*5

e. +.39


population. The sample size for sample 1 is (, while the sample arian!e is +*.3. 4or

sample 2, the sample size is *, while the sample arian!e is +(.5. e wish to test

whether the population arian!e of population 1 is greater than the population



a. 2.(2

". 3.22

!. 3.)*

d. 2.*5

&e. +.39

9(. Two samples are drawn, one ea!h from an independent normally distri"uted

population. The sample size for sample 1 is 11, while the sample arian!e is 51.2.



arian!e of population 2. hat would "e the !on!lusion to the test in this !ase, if we

test at the 5 leel of signifi!an!ea. re/e!t H)in faour of H1and !on!lude that the arian!e of population 1 is greater

than that of population 2

&". do not re/e!t H)in faour of H1and !on!lude that the arian!e of population 1 is

not greater than that of population 2

!. re/e!t H)in faour of H1and !on!lude that the arian!e of population 1 is not

greater than that of population 2

d. do not re/e!t H)in faour of H1and !on!lude that the arian!e of population 1 is


e. none of the a"oe

9*. Two samples are drawn, one ea!h from an independent normally distri"utedpopulation. The sample size for sample 1 is (, while the sample arian!e is +*.3. 4or


27/29

sample 2, the sample size is *, while the sample arian!e is +(.5. e wish to test

whether the population arian!e of population 1 is greater than the population

arian!e of population 2. hat would "e the !on!lusion to the test in this !ase, if we

test at the 5 leel of signifi!an!e

a. re/e!t H)in faour of H1and !on!lude that the arian!e of population 1 is greater

than that of population 2&". do not re/e!t H)in faour of H1and !on!lude that the arian!e of population 1 is

not greater than that of population 2

!. re/e!t H)in faour of H1and !on!lude that the arian!e of population 1 is not


d. do not re/e!t H)in faour of H1and !on!lude that the arian!e of population 1 is


e. none of the a"oe

9'. e hae two ma!hines that fill milk "ottles. e a!!ept that "oth ma!hines are

putting, on aerage, one litre of milk into ea!h "ottle. e suspe!t, howeer, that the

first ma!hine is !onsidera"ly less !onsistent than the se!ond, and that the olume ofmilk it deliers is more aria"le. e take a random sample of 1( "ottles from the first

ma!hine and 25 "ottles from the se!ond ma!hine and !ompute sample arian!es of

5.9ml2and 2.1ml2respe!tiely. e wish to test whether our suspi!ions are !orre!t at

the 5 signifi!an!e leel. hat is the !orre!t !on!lusion that !an "e made at the 5

signifi!an!e leel in this !ase

&a. re/e!t the null hypothesis and !on!lude that ma!hine 1 is less !onsistent than

ma!hine 2

". do not re/e!t the null hypothesis and !on!lude that there is no differen!e in

!onsisten!y "etween the two ma!hines

!. re/e!t the null hypothesis and !on!lude that ma!hine 2 is less !onsistent than

ma!hine 1

d. do not re/e!t the null hypothesis and !on!lude that ma!hine 2 is less !onsistent than

ma!hine 1

e. re/e!t the null hypothesis and !on!lude that there is no differen!e in !onsisten!y

"etween the two ma!hines

99. e hae two ma!hines that fill milk "ottles. e a!!ept that "oth ma!hines are


first ma!hine is !onsidera"ly less !onsistent than the se!ond, and that the olume of

milk it deliers is more aria"le. e take a random sample of 1( "ottles from the first

ma!hine and 25 "ottles from the se!ond ma!hine and !ompute sample arian!es of3.2ml2and 2.1ml2respe!tiely. e wish to test whether our suspi!ions are !orre!t at



a. re/e!t the null hypothesis and !on!lude that ma!hine 1 is less !onsistent than

ma!hine 2

&". do not re/e!t the null hypothesis and !on!lude that there is no differen!e in



ma!hine 1

d. do not re/e!t the null hypothesis and !on!lude that ma!hine 2 is less !onsistent than

ma!hine 1


28/29



1)). e hae two ma!hines that fill milk "ottles. e a!!ept that "oth ma!hines are


first ma!hine is !onsidera"ly less !onsistent than the se!ond, and that the olume ofmilk it deliers is more aria"le. e take a random sample of 1( "ottles from the first

ma!hine and 25 "ottles from the se!ond ma!hine and !ompute sample arian!es of

+.'ml2and 2.1ml2respe!tiely. e wish to test whether our suspi!ions are !orre!t at



&a. re/e!t the null hypothesis and !on!lude that ma!hine 1 is less !onsistent than

ma!hine 2

". do not re/e!t the null hypothesis and !on!lude that there is no differen!e in



ma!hine 1d. do not re/e!t the null hypothesis and !on!lude that ma!hine 2 is less !onsistent than

ma!hine 1



1)1. random sample is drawn from ea!h of two normally distri"uted populations.

The sample size for sample 1 is 1( and the sample standard deiation is 15. The

sample size for sample 2 is 13 and the standard deiation is 1). e wish to test at the

1) leel of signifi!an!e whether there is enough eiden!e to infer that the two

population arian!es differ. hat is the alue of the test statisti! in this !ase

a. 2.3(

". 2.(2

&!. 2.25

d. 1.21

e. 1.'(





population arian!es differ. hat is the alue of the test statisti! in this !asea. 2.3(

". 2.(2

!. 2.25

&d. 1.21

e. 1.'(





population arian!es differ. hat is the !on!lusion, "ased on a 1) signifi!an!eleel


29/29

a. e/e!t H)and !on!lude that the two population arian!es differ

". 4ail to re/e!t H1and !on!lude that the two population arian!es differ

&!. 4ail to re/e!t H)and !on!lude that the two population arian!es do not differ

d. 4ail to re/e!t H)and !on!lude that the two population arian!es differ

e. !!ept H)and !on!lude that the two population arian!es do not differ

1)+. random sample is drawn from ea!h of two normally distri"uted populations.




population arian!es differ. hat is the !on!lusion, "ased on a 1) signifi!an!e

leel

a. e/e!t H)and !on!lude that the two population arian!es differ

". 4ail to re/e!t H1and !on!lude that the two population arian!es differ

&!. 4ail to re/e!t H)and !on!lude that the two population arian!es do not differ

d. 4ail to re/e!t H)and !on!lude that the two population arian!es differ

e. !!ept H)and !on!lude that the two population arian!es do not differ

quiz 9 hypothesis testing for two populations

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