Question

Paired Samples t-test

Gregg Popovich, head coach of the San Antonio Spurs, had his top five scorers practice during the past week with the shooting coach Chip Engelland. They shot 100 free throws prior to working with Chip and then shot 100 free throws after working with Chip. Below are the total number of free throws made before and after working with Chip Engelland. Popovich wants to know if practicing with Chip increased their free throw making abilities. Use a p-value (α) of 0.05 to conduct the test.

Step 1: Populations, Distribution, and Assumptions

Population 1:

Population 2:

Distribution:

Hypothesis test to be used (Explain):

Step 2: Hypotheses

Research Hypothesis:

Symbolic Research Hypothesis:

Null Hypothesis:

Symbolic Null Hypothesis:

Before Chip	After Chip
90	94
77	82
64	85
87	97
88	95

5

Step 3: Characteristics of the Comparison Distribution (6 points)

Um (mean of means) = __________

SM= __________

#
1
2
3
4
5

Step 4: Critical Values

t critical, =____________-.

df= __________

Step 5: Calculate Test Statistic

t statistics =____________

Step 6: Make a Decision

Be sure to explain and also report your answer in APA format.

SS =________________

6

Effect Size

Calculate the effect size for the previous comparison. Cohen’s d = __________

Confidence Interval

Calculate the confidence interval

CI 90% = [ ________ , _________ ]

Answer 1

Step 1: Populations, Distribution, and Assumptions

Population 1: free throws prior to working with Chip

Population 2: free throws after working with Chip

Distribution: t distribution with degrees of freedom = 5 - 1 = 4

Hypothesis test to be used (Explain): Practicing with Chip increased their free throw making abilities

Step 2: Hypotheses

Research Hypothesis: Practicing with Chip increased their free throw making abilities

Symbolic Research Hypothesis: < 0

Null Hypothesis: Practicing with Chip did not increase their free throw making abilities

Symbolic Null Hypothesis: 0

Step 3: Characteristics of the Comparison Distribution (6 points)

Step 1: Values of d = Before Chip - After Chip are got as follows:

Values of d = Before Chip - After Chip = - 4, - 5, - 21, - 10, - 7

= - 47/5= - 9.4

d	d -	(d - )2
- 4	5.4	29.16
- 5	4.4	19.36
- 21	- 11.6	134.56
- 10	- 0.6	0.36
- 7	2.4	5.56
Total =		189.2

s_d = sqrt(189.2/4) = sqrt(47.3) = 6.877

Um (mean of means) =

SM= sd = 6.877

#
1					90 - 94 = - 4
2					77 - 82 = - 5
3					64 - 85 = - 21
4					87 - 97 = - 10
5					88 - 95 = - 7

Step 4: Critical Values

= 0.05

df = 5 - 1 = 4

t critical, = - 2.132

df= 4

Step 5: Calculate Test Statistic

t statistics = - 3.056

Step 6: Make a Decision

Since calculated value of t = - 3.056 is less than critical value of t = - 2.132, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that Practicing with Chip increased their free throw making abilities

Cohen's d is given by:

df = 4

= 0.10

From Table, critical values of t = 2.1318

SE = sd/

= 6.877/

= 3.0755

Confidence Interval:

- 9.4 (2.1318 X 3.0755)

= - 9.4 6.5564

= ( - 15.9564, - 2.8436)

So,

Answer is:

CI 90%: [ - 15.9564, - 2.8436]