Question

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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 Chp increased their free throw making abilities. Use a p-value (a) of 0.05 to conduct the test. Before Chip After Chip 90 94 77 82 64 85 87 97 88 95 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 Nu Hypothesis:

Answer 1

ANSWER:

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: \mu _{D} < 0

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

Symbolic Null Hypothesis: \mu _{D}\geq 0

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

Um (mean of means) = \bar{d}=-9.4

SM= sd = 6.877

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

56 is less than Step 4: Critical values d = 0,05 df = 5-1 = 4 t Critical , 2-2-132 df = 4 Step 5 : Calcolate Test statistic L = -905 7 -3.056 Salvo 6-877 6.877 t- Statistic =- 3.056. Step 6: Make a decision Since calculate value of t= - 3,0 56 PS . Critical value of ta-2.132, the difference is Significant Reject the null hypothess. Conclusion: The data Support the claim that practicing with chip increased their free throw making ability Cohen's is given by: de 904 67877. 204 = 103669 df z 4 2= o-10 from table, Critical value of ts I 21313

. = 6-877 = 3.0755 Confidence intervats -9.4 I (21318x30755) 3-9041 6-5564 = (-15,9564,-28436) So, .. Answer is Cl 90% · [-15.9564,-2.8436]