T-tests paired or independent?

A medical assistant sampled the blood pressures of 20 randomly selected patients with high blood pressure before and after they receive a dose of a new medicine. Which hypothesis test should she run?

• Paired t-test. Since the patients are the same in both sample 1 and sample 2, the two samples are linked.

• independent-sample t-test. Since the blood pressures were taken for 20 patients in sample 1 and the same 20 patients in sample 2, use a two-sample t-test to see if the results are statistically significant.

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A researcher gave one group of people an active drug and gave a different group of people an inactive placebo, then compare the blood pressures between the groups. Which test should he run to determine the efficacy of the active drug?

• Paired t-test. Since there is a group with the active drug and another with the inactive drug, he may pair the two two groups if the sample sizes are the same.

• independent-sample t-test. Since the blood pressures were taken for patients in sample 1 and different patients in sample 2, use a two-sample t-test to see if the results are statistically significant.

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Does the mean height of female college students significantly differ from the mean height of male college students?

• Paired t-test. Test whether the difference of the means of one male paired with one female is equal to 0.

• independent-sample t-test. Test whether the mean height of female college students is different than the mean height of male college students.

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If you measure the weight of male college students before and after each subject takes a weight-loss pill, is the mean weight loss significant enough to conclude that the pill works?

• Paired t-test. Test whether the mean of the differences in weights between the male college students before they took the weight-loss pill and after they take the weight loss is significant to conclude the pill works.

• independent-sample t-test. Compare the mean weights of the males both before and then after the weight-loss pill is taken to see if there is a decrease in weight between the groups overall.

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I run a paired t-test for 15 sets of first grade twins reading abilities if one twin used a computer program tutor and the other did not, and get a p-value of 0.02, what does this mean for a significance level of 0.05?

• Reject the null hypothesis. There is evidence at the 0.05 level that the computer program tutor is more effective at raising reading scores.

• Fail to reject the null hypothesis. There is no evidence at the 0.05 level that the computer program tutor is more effective at raising reading scores.

• This was not the proper use of a paired t-test; no conclusions can be drawn from this test.

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CCSS.HSS.IC.B.5

A manufacturer of gloves wants to determine if a special type of wool gloves lasts longer than the cotton gloves they manufacture. He makes pairs of gloves in which the left hand is cotton and the right hand is wool. We sample 24 women who wear these pairs of gloves, then use a paired t-test to find the mean of the differences in wear between the right glove and left glove; we get a p-value of 0.043. At the 0.05 level, what should we conclude?

• Reject the null. There is evidence at the 0.05 significance level that the wool gloves lasts longer than the cotton glove.

• Fail to reject the null. There is evidence at the 0.05 significance level that the wool glove lasts longer than the cotton glove.

• Fail to reject the null. There is no evidence at the 0.05 significance level that the wool glove lasts longer than the cotton glove.

• We cannot conclude anything because a paired t-test was not the appropriate test to run for this sample.

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