March 5th and 6th Check

1.  Data set is 2, 2, 25, 9, 25, 9, 15, 5, 20 What is the n?

9

2.  Data set is 2, 2, 25, 9, 25, 9, 15, 5, 20 What is the M?

12.44

3.  Data set is 2, 2, 25, 9, 25, 9, 15, 5, 20 What is the range?

2 – 25 25-2= 23 (25 – 2) + 1 = 24

Data set is 2, 2, 25, 9, 25, 9, 15, 5, 20 4. What is Q1?

Rank Order2, 2, 5, 9, 9, 15, 20, 25, 25

2, 2, 5, 9, 9, 15, 20, 25, 25

2 + 5 = 7  7/2 = 3.5

Q1 = 3.5

Excel... Q1 = 5

Data set is 2, 2, 25, 9, 25, 9, 15, 5, 20 5. What is Q2?

Rank Order2, 2, 5, 9, 9, 15, 20, 25, 25

2, 2, 5, 9, 9, 15, 20, 25, 25

Q2 = 9

Data set is 2, 2, 25, 9, 25, 9, 15, 5, 20 6. What is Q3?

Rank Order2, 2, 5, 9, 9, 15, 20, 25, 25

2, 2, 5, 9, 9, 15, 20, 25, 25

20 + 25 = 45  45/2 = 22.5

Q3 = 22.5 Excel... Q3 = 20

Data set is 2, 2, 25, 9, 25, 9, 15, 5, 20 7. What is the Interquartile Range?

Q1 = 3.5Q3 = 22.5

IQR = 22.5 – 3.5 = 19        IQR = (22.5 – 3.5) + 1 = 20

Excel... IQR = 15 16

Use the information below to answer items 8-9: Group A: M = 20.00, S = 2.00Group B: M = 33.33, S = 3.418.  What is the z-score of a person with a raw score of 

20 in Group A?

z = (x  - M)/s

z = (20 – 20)/2.00 z = 0/2.00z = 0

Use the information below to answer items 8-9: Group A: M = 20.00, S = 2.00Group B: M = 33.33, S = 3.419. What is the z-score of a person with a raw score of

22 in group B?

z = (x  - M)/s

z = (22 – 33.33)/3.41 z = -11.33/3.41z = -3.32

10. Reading Test: M = 30.00, S = 3.00 Math Test: M = 40.00, S = 4.00

John has a raw score of 33 on reading and 34 on math? Based on z-scores, which test did John score higher on?

z = (x  - M)/s

zr = (33 – 30.00)/3.00 zm = (34 – 40.00)/4.00

zr = 3.00/3.00 zm = -6.00/4.00

zr = 1.00 zm = -1.50

John scored higher on Reading

Using the information below, answer items 11 -14 219 Clinicians were surveyed as part of a study to determine the rates of including parents in the process of treating children and adolescents with cognitive-behavioral therapies. The results of the data collection are shown below:Rates of Including Mothers and Fathers in Treatment with Children and Adolescents

VariableFather involved  f

(% of  time)

M

(% of  time)

 S

Mother involved f

(% of  time)

M

(% of  time)

S

Intact Family 86 39.46 26.85 136 62.00 26.07

Single-Parent Family 46 21.22 23.13 122 55.64 24.53

Children (12 and under) 65 29.79 23.36 143 65.45 25.13

Adolescents (13-18) 68 31.04 23.27 113 51.39 26.24

11. Which parent was reportedly involved in therapy most often?

Mother or FatherMother or Father

12. Which value is more variable?

a. Mothers of Adolescents

b. Fathers of Intact Families

c. Mothers of Intact Families

d. Fathers of Children

a. Mothers of Adolescents

b. Fathers of Intact Families

c. Mothers of Intact Families

d. Fathers of Children

“And” & “Or”

• When describing an event for which we would like to compute a probability, two words will often be used– And

• And is used to describe the intersection of two events• Both events have to occur at the same time

– e.g. The Car is Black and it is an Automatic

– Or• Or is used to describe the union of two events• Either one or the other events can occur

– e.g. The Car is Black or The Car is an Automatic

Multiplication Rule

• For independent events:

• For dependent events:

)()() and ( BPAPBAP

)|()() and ( ABPAPBAP

Examples

04.050

4

50

26)A(*)B( utoPlackP

125.05.05.05.0)(*)(*)( GPGPGP

0625.052

13

52

13)H(*)H( 21 eartPeartP

0588.051

12

52

13)H|H(*)H( 121 earteartPeartP

• Compute the following Probabilities:– P(Black and Auto)

– P(GGG) – Assume P(G) = 0.5

– P(Heart, Heart) – replace - Independent

– P(Heart, Heart) – do not replace - Dependent

Additive Rule

) and ()()()or ( BAPBPAPBAP

We subtract off the P(A and B), because we are in a sense adding it twice, once in the P(A) and once in the P(B).

However, if events A and B are Mutually Exclusive, this formula becomes:

)()()or ( BPAPBAP

Mutually Exclusive

• Two events are mutually exclusive if they cannot occur at the same time– If they cannot occur at the same time, then the

P(A and B) = 0• Which one of these two events is mutually

exclusive?– P(Female or 25 yrs old)– P(Heart or Diamond)

Rolling Two Dice

• P(Sum of Dice is 5)?– P(4,1 or 3,2 or 2,3 or 1,4)

11.036/4

36/136/136/136/1)5(

36/1)4,1(

36/1)3,2(

36/1)2,3(

36/1)1,4(

)()()or (

sumP

P

P

P

P

BPAPBAP

Example

• The probability that a patient is admitted to the hospital for surgery is P(S) = 0.12. The probability that a patient is admitted receives OB Services is P(O) = 0.16. The probability that they receive both treatments is P(S&O) = 0.02. What is the probability they receive either surgery, obstetrics or both P(S or O)?

.12 + .16 - .02 = 0.26P(S or O) = P(S) + P(O) – P (S & O) = .12 + .16 - .02 = 0.26

Using the information below, answer items 11 -14 219 Clinicians were surveyed as part of a study to determine the rates of including parents in the process of treating children and adolescents with cognitive-behavioral therapies. The results of the data collection are shown below:Rates of Including Mothers and Fathers in Treatment with Children and Adolescents

VariableFather involved  f

(% of  time)

M

(% of  time)

 S

Mother involved f

(% of  time)

M

(% of  time)

S

Intact Family 86 39.46 26.85 136 62.00 26.07

Single-Parent Family 46 21.22 23.13 122 55.64 24.53

Children (12 and under) 65 29.79 23.36 143 65.45 25.13

Adolescents (13-18) 68 31.04 23.27 113 51.39 26.24

13. Using empirical probability:What is the probability Fathers will be involved in the therapy of children or adolescents?

Sample Space = 219P(Child or Adols) =  65/219 + 68/219

  =  133/219  = .6073  = .61  = 61%

14. Using empirical probability:What is the probability Mothers or Fathers will be involved in the therapy of children?

Sample Space = 219P(Mo or Fa) =  143/219 + 65/219

  =  208/219  = .949  = .95  = 95%

15. For items 15 and 16,

I have a bag of marbles that are red and blue. Describe the sample space if I pull two marbles from the bag, one at a time. Use R = Red and B = Blue

Sample Space = { RR, RB, BB, BR}

16. Using Classical Probability, what is the chance that I will pull out a red marble first if I pull two marbles from the bag, one at a time.

Sample Space = {RR, RB, BB, BR}Event = {RR, RB}P(E) = 2/4 = ½ = .50 = 50%