# Nine runners agree to participate in a study on two

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 randomly 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 (1 point)
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Which of the following statements is/are true?
(You must select all of the correct answer choices and none of the incorrect answer choices in
order to receive credit. No partial credit will be given.)
In order to conduct a matched pairs t test, we must assume that differentes in running
times are normally distributed.
In order to conduct a matched pairs t test, we must assume that running times with Brand
A shoc and Brand B shoe arc both normally distributed.
For any two runners, running times with Brand A shoc are independent.
For cach runner, running times with Brand A shoc and Brand B shoc are independent.
Question 2 (1 point)
We would like to construct a 99% confidence interval for the true mean difference in running
times with Brand A and Brand B shoes. WWhat is the margin of error for the confidence interval?
Keep 4 decimal places in intermediate calculations and report your final answer to 2 decimal
places.
Your Answer:
Answer
Question 3 (1 point)
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At the 5% level of significance, we would like to determine if there is evidence that the true
mean running times for the two brands differ. What is the P-value for the appropriate test of
significance?
between 0.01 and 0.02
between 0.02 and 0.04
between 0.04 and 0.05
between 0.05 and 0.10
between 0.10 and 0.20
Question 4 (1 point)
What is the interpretation of the P-value in the previous question?
O A) If the true mean running time were equal for the two brands, the probability of
incorrectly concluding that the means differ would be (your answer to previous
question).
O 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
observing a sample mean of differences at least as cxtreme as -0.27 would be (your
answer to previous question).
D) The probability that the true mean running time is equal for the two brands is (your
answer to previous question).
O 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 5 (1 point)
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We will commit a Type II error in the hypothesis test in Question 3 if we conclude that there is:
O A) sufficient evidence that average running times for the two brands differ when in fact
average running times for the two brands do differ.
O B) insufficient evidence that average running times for the two brands differ when in fact
average running times for the two brands do differ.
O 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.
O D) sufficient evidence that average running times for the two brands differ when in fact
there is no difference in average running times for the two brands.
E) insufficient 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.
OF) insufficient evidence that there is no difference in average running times for the two
brands when in fact there is no difference in average running times for the two brands.
G) sufficient evidence that there is no difference 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 average running times for the two brands differ when in fact
there is no difference in average running times for the two brands.
Question 6 (1 point)
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Suppose we had instead used the critical value method to conduct the test in Question 3. We
would reject Ho if:
Otz 2.306 orts-2.306
Otz 1.860 or t s-1.860
Otz 1.860
Ot2 2.306
Ots-2.306
Ots-1.860