exercises on significance z

8/14/2019 Exercises on Significance Z

1/5

Solution:

sample-1 (n1= 100 ) (p1= 20 ) (q1= 80 )

sample-2 (n2= 100 ) (p2= 30 ) (q2= 70 )

Ho:

=SQRT OF

2SE (p1-p2)= 12.16552506

As the Difference of the Two proportion is less than 2SE,

there is no statitical significance at 5% level

There is no evidence that the two sample Typoid

Mortality Rates are different from each other.

Null Hypothesis : There is no Difference between the Twosample proportions.

(37)= 6.08276253

10Difference of Two Proportions=

Inference:

Exercise-1

The Typhoid Mortality of on sample of 100 is 20 % and in

another sample of 100 is 30 %. Is the difference in

moratality rate significance?

Standard Error of (p1-p2)=SQRT of [(p1Xq1)/n1+(p2Xq2)/n2]

SE (p1-p2)=SQRT of [(p1Xq1)/n1+(p2Xq2)/n2]

p1=p2

=,*(p1=20)X(q1=80)/(n1=100)+*(p2=30)X(q2=70)/(n2=1


2/5

Solution:

p in %

sample-1 46

sample-2 22

sample-1 (n1= 50 ) (p1= 46 ) (q1= 54 )

sample-2 (n2= 350 ) (p2= 22 ) (q2= 78 )

Ho:

=

There is Statistical evidence to show that the two Schools A & B are

different in the prevalence of Tonsilities.

q in %

54

78

No. of Tonsilectomy

23

77

24As the Difference of the Two proportion is more than 2SE, there is

statistical significance at 5% level.

Difference of Two Proportions=

2SE= 14.7760424

Inference:

=SQRT OF (54.5829)= 7.3880212

Size of sample

50

350

Table-1 Showing the No. Tonsilectomy cases & calculated Ps& qsin %

Table-2 Showing the calculated Ps& qsin %

In school -A, tonsilectomy was done in 23 students out of 50while in

another school B it was done in 77 out of . Find out whether the

difference between the two Tonsilectomy proportions is significance?

p1=p2

Null Hypothesis : There is no Difference between the Two sample

proportions.



{[(p1=46)X(q1=54)/(n1=50)]+[(p2=22)X(q2=78)/(n2=350)]}


3/5

Solution:

p in %

sample-1 50

sample-2 61.4286

sample-1 (n1= 50 ) (p1= 50 ) (q1= 50

sample-2 (n2= 350 ) (p2= 61.429 ) (q2= 38.6Ho:

=

=SQRT OF

Size of sample No. of Students with

Whooping Cough

q in

50 25 5

Table-1 Showing the No. of Students with Whooping Cough & calculated Ps& qsin

(56.7697)= 7.53457

350 215 38.5

p1=p2

Null Hypothesis : There is no Difference between the Two sample

proportions.


Table-2 Showing the calculated Ps& qsin %

15.069131022SE(p1-p2)=

Exercise-3

As the Difference of the Two proportion is less than 2SE, there is no

statistical significance at 5% level.

There is no Statistical evidence that the two Schools A & B are dif

in the prevalence of Whooping Cough. ie. Similar staus quo i

prevalence of Whooing Cough between the Two Schools A & B.

Inference:

Difference of Two Proportions= 11.4286


In school -A , there is Whooping Cough in 25 students out of 50 while the sc

B, there is Whooping Cough in 215 out of 350. Is the Difference of the Preval

of Whooping Cough between the Two Schools A & B , Statistically Significant

{[(p1=50)X(q1=50)/(n1=50)]+[(p2=61.4286)X(q2=38.5714)/(n2=350)]}


4/5

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erent

the

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?


5/5

Solution:sample-1 (n1= 100 ) (p1= 20 ) (q1= 80 )

sample-2 (n2= 100 ) (p2= 30 ) (q2= 70 )

Ho:

sample-1

sample-2

Total

sample-1

sample-2

Total

2=

=

=

=

=

Inference: There is no Statistical Siginificance between the Two Samples in the

'Typoid -Effect'

The 5% Tabular 2 Value with 1 Degrees of Freedom=3.84

As the Calculated Chi-Square Value=1.3333 which is Less thanThe 5% Tabular 2

Value with 1 Degrees of Freedom=3.84 , the Null Hypothesis is Accepted

The Test Statistic is Chi-Square.

(O-E)2/E [Wheras, O= Observed cell value & E=Expected Cell Value]

1.3333

(20-25)^2/25+(80-75)^2/75+(30-25)^2/25+(70-75)^2/75

(25/25)+(25/75)+(25/25)+(25/75)

1+0.3333+0+0

50 150 200

200

No. of Typoid Deaths No. of cases without the

Deaths due to Typoid

20

30

50 150

The Expected Cell11Value=(First Row Total X First Column Total)/N

No. of Typoid Deaths No. of cases without the

Deaths due to Typoid

Total No. of

Typoid Cases

Expected Cell Frequencies in 2x2 Contingency Table:

The Expected Cell12Value=(First Row Total X Secont Column Total)/N

Exercise-4

The Typhoid Mortality of on sample of 100 is 20 % and in another sample of 100 is 30 %.

Is the 'Typoid - effect' between the two Samples significantly different?

Let us form the 2X 2 contingency Table for the Two Samples vs Typoid Deaths & No

Death with the Typoid

80

70

Observed Cell Frequencies in the 2x2 Contingency Table:

There is no siginificant difference between the Two Samples in quantityterms

Total No. of

Typoid Cases

100

100

25 75 100

The Expected Cell22Value=(Second Row Total X Second Column Total)/N

The Expected Cell21Value=(Second Row Total X First Column Total)/N

25 75 100

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