Question

Eight runners were convinced that the average difference in their individual times for running one mile versus race walking one mile was at most 2 minutes. Below are their times. Do you agree that the average difference is at most 2 minutes? Conduct a hypothesis test at the 5% level.

Running time (minutes)	Race walking time (minutes)
5.3	7.5
5.7	9.5
6.2	10.2
4.8	6.9
7.1	8.9
4.2	9.5
6.1	9.4
4.4	7.9

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

1) State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)

2) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)

3) What is the p-value? (Round your answer to four decimal places.)

4) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =

Answer 1

1)

Here we have paired data so paired t test will be used.

Let d =Race walking time-Running time

Following table shows the calculations:

Race walking time	Running time	d	(d-mean)^2
7.5	5.3	2.2	1.1025
9.5	5.7	3.8	0.3025
10.2	6.2	4	0.5625
6.9	4.8	2.1	1.3225
8.9	7.1	1.8	2.1025
9.5	4.2	5.3	4.2025
9.4	6.1	3.3	0.0025
7.9	4.4	3.5	0.0625
Total		26	9.66

2)

3)

4)

α = 0.05

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