Reference no: EM132856534

Question 1-5 as 1 full question

Nine runners agree to participate in a study on two brands of shoes on the time to run a race. The runners are asked to run a 10-kilometer race on each of two consecutive weeks. In one of the races, the runners wear one brand of shoe and in the other a different brand(with the order raandomly determined). the differences in running times (Brand A minus Brand B) have a mean of -0.27 minutes with a standard deviation of 0.4 minutes.

Question 1 We would like to conduct a 99% confidence interval for the true mean difference in running times with Brand A and Brand B shoes. What is the margin of error for the confidence interval?

Keep 4 decimal places in the intermediate calculations and report your final answer to 2 decimal places.

Question 2

At the 5% level of significance, we would like to determine if there is a evidence that the true mean running times for the two brand differ. What is the P-value for the appropriate test of significance?

a. between 0.01 and 0.02

b. between 0.02 and 0.04

c. between 0.04 and 0.05

d. between 0.05 and 0.10

e. between 0.10 and 0.20

Question 3

What is the interpretation of the P-value in the previous question?

a. If the true mean running time were equal for the two brands, the probability of incorrectly concluding that the means would be(your answer to the previous question).

b. The probability that the true mean running time differs for the two brands is (your answer to previous question)

c. If the true mean running time were equal for the two brands, the probability of observiing a sample mean of differences at least as extreme as -0.27 would be(your answer to previous question).

D. The probablility that the true mean running time is equal for the two brands(your answer to the previous question)

E. If the true mean running time differed for the two brands, the probability of observing a sample mean of differences at least as extreme as -0.27 would(be your answer to previous question

Question 4

We will commit a Type II error in the hypothesis test in Question 2 if we conclude that there is:

A. Sufficient evidence that average running times for the two brands differ when in fact average running times for the two brands do differ.

B. Insufficient evidence that average running times for the tow brand differ when in fact average running times for the two brands do differ.

C. sufficient evidence that there is no difference in average running times for the two brands when in fact average running times for the two brands do differ.

D. sufficient evidence that the average running times for the two brands differ when in fact there is no differnce in average running times for the two brands.

E. insufficient evidence that there is no differnce in average times for the two brands when in fact average running times for the two brands do differ.

F. Insufficient evidence that there is no difference in average running times for the two brands when in fact there is no differnce in average running times for the two brands.

G. sufficient evidene that there is no differnce in average running times for the two brands when in fact there is no difference in average running times for the two brands.

H. Insufficient evidence that the average running times for the two brands differ when in fact there is no differnce in average running times for the two brands.

Question 5

Suppose we had instad used the critical value method to conduct the test in question 2. We would reject Ho if:

a. t≥ 2.306 or t≤ -2.306

b. t≥ 1.860 or t≤ -1.860

c. t≥ 1.860

d. t≥ 2.306

e. t≤ -2.306

f. t≤ -1.860