Anna decided to sort the data by gender, and by ACT score. She used an ACT score

Question

Anna decided to sort the data by gender, and by ACT score. She used an ACT score of 22 as her cutoff since this is the national average ACT score. The table below summarizes the 20 individuals in the sample.

Question: If one individual is randomly selected from these 20 people represented in the table below:

ACT Score of

22 or Less

ACT Score Greater than 22

Total

Male

5

6

11

Female

1

8

9

Total

6

14

20

a. What is the probability that the selected individual has an ACT score greater than 22 or is a male?

b. What is the probability that the selected individual is has an ACT score greater than 22 and is a female?

c. Given that the selected individual has an ACT score of 22 or less, what is the probability that the individual is a female?

d. Given that the selected individual is female, what is the probability that the individual has an ACT score of 22 or less?

e. What is the probability the selected individual has an ACT score of 22 or less?

f. What is the probability that the selected individual has an ACT score greater than 22?

g. In the table above, what type of data are "male" and "female"? (circle one)

QUALITATIVE or QUANTITATIVE

h. In general, what type of data are ACT scores? (circle one)

QUALITATIVE or QUANTITATIVE

Once Anna had sorted the sample data according to males and females, she found the following:

Mean ACT Score

Standard Deviation

n

Males

23.09

3.88

11

Females

25.889

2.522

9

The numbers in the table are called (3 pts): (circle one)

STATISTICS or PARAMETERS

Anna’s 2nd Question: Do males who participate in the workshop score significantly lower on the ACT than females who participate in the workshop?

Based on the results in the table directly above, is there sufficient evidence at the 0.05 level of significance to believe males participating in the workshop score significantly lower on the ACT than females who participate in the workshop?

Determine the type of sampling method used for this data (3 pts): (circle one)

DEPENDENT or INDEPENDENT

Perform the appropriate hypothesis test using both Classical and P-value Approach. (4 + 2 + 4 + 6 + 4 + 4 = 24 pts)

Step 1: Write the null and alternative hypothesis.

Ho: ______________________________ H1: ______________________________

Step 2: State the level of significance, = ______________

Step 3: Calculate the test statistic. ______________________________________________________

Work or calculator keys used: ______________________________________________________________

Step 4a: Determine critical value(s) and rejection region(s): Reject Ho if _________________________

_____________________________________________________________________________

(Draw and label a distribution curve to help you.)

Step 4b: Determine the p-value: _________________________________________________________

Step 5: Make comparisons and state your decision: __________________________________ because

____________________________________________________________________________

Step 6: Write your conclusion in words ____________________________________________

_____________________________________________________________________________

Anna’s 3rd Question: Is the average ACT score of students participating in the workshop significantly higher than 22? (She chose 22 because it was the national average ACT score.)

To do this, she used her posttest sample of 20 students.

Ending (post-test sample)

a. Mean =24.35

b. Standard deviation =3.4681

c. Variance =12.0275

d. Median =24

e. Minimum value =17

f. Maximum value =32

g. Range =15

h. Quartile 1 (Q1) =22

i. Quartile 3 (Q3) =26

j. Interquartile Range =4

She calculated descriptive statistics for their posttest ACT exam scores. These are: . 24.350, 3.558, 20 x s n

***Find the 95% confidence interval for the mean posttest ACT score of all students participating in the workshop.

a) Use the correct formula and set up the confidence interval. You may use the calculator to finish it.

Confidence Interval setup: _______________________________________________________________

Confidence interval: ____________________________________________________________________

Calculator commands: ___________________________________________________________________

b) Interpret your confidence interval—What does it tell you about the average ACT score of students participating in the workshop? ______________________________________________________

_______________________________________________________________________________

At the 0.05 significance level, does Anna have sufficient evidence that the mean posttest ACT score of her workshop participants is greater than 22? Use the statistics given at the top of the page. Assume ACT scores are normally distributed and perform the appropriate hypothesis test using both Classical and P-value Approach. (4 + 2 + 4 + 6 + 4 + 4 = 24 pts)

Step 1: Write the null and alternative hypothesis.

Ho: ______________________________ H1: ______________________________

Step 2: State the level of significance, = ______________

Step 3: Calculate the test statistic. ______________________________________________________

Work or calculator keys used: ______________________________________________________________

Step 4a: Determine critical value(s) and rejection region(s): Reject Ho if _________________________

_____________________________________________________________________________

(Draw and label a distribution curve to help you.)

Step 4b: Determine the p-value: _________________________________________________________

Step 5: Make comparisons and state your decision: ___________________________________ because

_____________________________________________________________________________

Step 6: Write your conclusion in words: __________________________________________________

_____________________________________________________________________________

ACT Score of

22 or Less

ACT Score Greater than 22

Total

Male

5

6

11

Female

1

8

9

Total

6

14

20

Explanation / Answer

Please one question at a time.

Here' the answer to all parts of the question :

a. P( ACT >22 or a male) = (14+11-6 / 20) = .95

b. P(ACT>22 or a female) = (9+14-8 /20) = .75

c. P( given ACT=<22 is female) = 1/6 = .167

d. P( given female, ACT=<22) = 1/9 = .1111

e. P(ACT=<22) = 6/20 = .30

f. P(ACT>22) = 14/20 = .70

g. Female and male is Qualitative data. Categorical data is always qualitiative

h. Numerical data is always Quantitative data

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