Question

Jessica runs a mile in 7 minutes, on average, with a standard deviation of 0.3. She decided to see if using new shoes improves her time. She used the new shoes for 14 runs. For those 14 runs, Jessica got an average of 6.9 minutes. She wants to know if the new shoes helped her run a faster mile. Which of the answer choices shows the correct first three steps of a one-mean hypothesis test at the 5% significance level?

Select the correct answer below:

A) H0:μ=7; Ha:μ<7, which is a left-tailed test.

α=0.05.

z0=7−6.9140.3√≈0.004.

B) H0:μ=7; Ha:μ>7, which is a right-tailed test.

α=0.05.

z0=6.9−7140.3√≈−0.004.

C)H0:μ=6.9; Ha:μ<6.9, which is a left-tailed test.

α=0.05.

z0=7−6.90.314√≈1.247.

D)H0:μ=7; Ha:μ>7, which is a right-tailed test.

α=0.05.

z0=6.9−70.314√≈−1.247.

E) H0:μ=6.9; Ha:μ>6.9, which is a right-tailed test.

α=0.05.

z0=7−6.90.314√≈1.247.

F) H0:μ=7; Ha:μ<7, which is a left-tailed test.

α=0.05.

z0=6.9−70.314√≈−1.247.

Answer 1

Given that Jessica runs a mile in = 7 minutes, on average, with a standard deviation of = 0.3. She decided to see if using new shoes improves her time. She used the new shoes for n = 14 runs. For those 14 runs, Jessica got an average of = 6.9 minutes.

F) Based on the given details the hypotheses are:

Based on the hypothesis it will be a left-tailed test.

The level of significance is given as α=0.05.

Test Statistic is calculated as: