Natasha is a physician looking to determine whether a supplement is effective in helping men lose weight. She takes a random sample of overweight men and records their weights before the trial. Natasha then prescribes the supplement and instructs them to take it for four weeks while making no other lifestyle changes. After the four-week period, she records the weights of the men again. Suppose that the data were collected for a random sample of 6 men, where each difference is calculated by subtracting the weight before the trial from the weight after the trial. Assume that the populations are normally distributed. The test statistic is t≈−2.795, α=0.05, the corresponding rejection region is t<−2.015, 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 weight of men after the trial and the weight before the trial is less than zero?A) Reject the null hypothesis that the true mean difference between the weight of men after the trial and the weight before the trial is equal to zero.B) Fail to reject the null hypothesis that the true mean difference between the weight of men after the trial and the weight before the trial is equal to zero.C) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the weight of men after the trial and the weight before the trial is less than zero.D) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the weight of men after the trial and the weight before the trial is greater than zero.

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Asked Jun 17, 2019
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Natasha is a physician looking to determine whether a supplement is effective in helping men lose weight. She takes a random sample of overweight men and records their weights before the trial. Natasha then prescribes the supplement and instructs them to take it for four weeks while making no other lifestyle changes. After the four-week period, she records the weights of the men again. Suppose that the data were collected for a random sample of 6 men, where each difference is calculated by subtracting the weight before the trial from the weight after the trial. Assume that the populations are normally distributed. The test statistic is t≈−2.795, α=0.05, the corresponding rejection region is t<−2.015, 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 weight of men after the trial and the weight before the trial is less than zero?

A) Reject the null hypothesis that the true mean difference between the weight of men after the trial and the weight before the trial is equal to zero.

B) Fail to reject the null hypothesis that the true mean difference between the weight of men after the trial and the weight before the trial is equal to zero.

C) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the weight of men after the trial and the weight before the trial is less than zero.

D) Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to suggest that the true mean difference between the weight of men after the trial and the weight before the trial is greater than zero.

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Expert Answer

Step 1

Test statistic results:

For testing whether a supplement is effective in helping men lose weight or not, it is given to assume that the populations are normally distributed.

Null and alternative hypotheses:

Null hypothesis:

H0: µd = 0

That is, the true mean difference between the weight of men after the trial and the weight before the trial is equal to zero.

Alternative hypothesis:

Ha: µd < 0

That is, the true mean difference between the weight of men after the trial and the weight before the trial is less than zero.

Significance level, α = 0.05.

t-statistic = −2.795

Rejection region, tcrit = −2.015

Step 2

Decision Rule:

If t > tcrit, reject null hypothesis.

Here, t-statistic < tcrit. Hence, we fail to reject null hypothesis at 0.05 significance level.

Statement that is accurate for this hypothesis test:

According to the given null hypothesis, the tr...

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