Question

Single Sample t-Test

Coach Brown is training his runners for an upcoming race, but he is concerned about their pace. He takes down sample times from his top 7 runners to compare it to his all-time standard race speed of 7.9 minutes per kilometer (μ). The sample times from his runners were 8.55 minutes per kilometer (M) with a standard deviation estimate of 0.78 (s).

Based on this data, complete the six steps of hypothesis testing given that our research question is: “Did the speed of the top 7 runners have a statistical difference compared to the Coach’s all-time standard race speed?”

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:

Step 3: Characteristics of the Comparison Distribution

UM (mean of means) = __________

SM= __________

2

Step 4: Critical Values

T critical =_______________________

DF = __________

Step 5: Calculate Test Statistic

T statistics =____________

Step 6: Make a Decision

Be sure to explain.

Effect Size

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

Confidence Interval

Calculate the confidence interval

CI 90% = [ ________ , _________ ]

3

Answer 1