Question

Asked Jun 18, 2019

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An executive believes that a new energy drink his company developed will increase an individual's stamina. In order to test this, he selects random individuals and times how long they can run without stopping. He then instructs the individuals to drink the energy drink for two weeks. After the two weeks, he times how long they can run again without stopping. Suppose that data were collected for a random sample of 35 people, where each difference is calculated by subtracting the time spent running before the two-week period from the time spent running after the two-week period. Assume that the times are normally distributed. The test statistic is t≈6.298, α=0.01, the corresponding rejection region is t>2.441, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd>0.

Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero?

Select all that apply:

A) Fail to reject the null hypothesis that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is equal to zero.

B) Reject the null hypothesis that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is equal to zero.

C) Based on the results of the hypothesis test, there is not enough evidence at the α=0.01 level of significance to suggest that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero.

D) Based on the results of the hypothesis test, there is enough evidence at the α=0.01 level of significance to suggest that the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero.

Step 1

**Paired t-test statistic results:**

For testing whether the new energy drink increase an individual’s stamina, 35 random individuals run times without stopping before and after 2 weeks of consuming the drink has been checked.

Let’s assume that the times are normally distributed.

**Null and alternative hypotheses:**

*Null hypothesis:*

*H*_{0}: µ_{d} = 0

That is, the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is equal to zero.

*Alternative hypothesis:*

*H*_{a}: µ_{d} > 0

That is, the true mean difference between the time spent running after the two-week period from the time spent running before the two-week period is greater than zero.

Significance level, *α* = 0.01.

*t*-statistic = 6.298.

Rejection region, *t*_{crit} > 2.441.

Step 2

**Decision Rule:**

If *t* > *t*crit, reject null hypothesis.

Here, *t-*statistic(=6.298) > *t*crit(=2.441).

Hence, **reject null hypothesis at 0.01 significance level**.

**Statement that is accurate for this hypothesis test:**

According to the hypotheses, the true mean difference betwee...

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