A study of road rage asked separate random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0 to 20. Are the conditions for performing a two-sample t test satisfied?

• Maybe; we have independent random samples, but we need to look at the data to check Normality.
• No; road rage scores in a range between 0 and 20 can’t be Normal.
• No; we don’t know the population standard deviations.
• Yes; we have two independent random samples and large sample sizes.

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CCSS.HSS.ID.A.4

The power take off drive line on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The drive line is covered by a shield in new tractors, but for a variety of reasons, the shield is often missing on older tractors. Two types of shields are the bolt-on and the flip-up. It was believed that the bolt-on shield was perceived as a nuisance by the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and maintenance and may be left in place. In a study initiated by the U.S. National Safety Council, random samples of older tractors with both types of shields were taken to see what proportion of shields were removed. Of 183 tractors designed to have bolt-on shields, 35 had been removed. Of the 136 tractors with flip-up shields,15 were removed. We wish to perform a test of H0: pb = pf versus Ha: pb > pf, where pb and pf are the proportions of all tractors with the bolt-on and flip-up shields removed, respectively. Which of the following is not a condition for performing the significance test?

• Both populations are Normally distributed.
• The data come from two independent samples.
• Both samples were chosen at random.
• The counts of successes and failures are large enoughto use Normal calculations.

At a baseball game, 42 of 65 randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence interval for the difference in population proportions(game − concert) is (−0.154, 0.138). Which of the following gives the correct outcome of the researcher’s test of the claim?

• Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.
• Because the center of the interval is –0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.
• Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.
• Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

Researchers are interested in evaluating the effectof a natural product on reducing blood pressure.This will be done by comparing the mean reductionin blood pressure of a treatment (natural product) group and a placebo group using atwo-sample t test. The researchers would like tobe able to detect whether the natural product reduces blood pressure by at least 7 points more,on average, than the placebo. If groups of size 50 are used in the experiment, a two-sample t testusing a = 0.01 will have a power of 80% to detect a 7-point difference in mean blood pressure reduction.If the researchers want to be able todetect a 5-point difference instead, then the power of the test

• would be less than 80%.
• would be greater than 80%.
• would still be 80%.
• could be either less than or greater than 80%, dependingon whether the natural product is effective.

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.

• 2-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.

• 1-sample t-test. The medical assistant should compare the mean of the first sample of 20 patients to the mean of the second sample of 20 patients.

• 2-sample t-test. There is no natural pairing between the two samples.

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.

• 2-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.

• 1-sample t-test. The researcher should compare the mean of the first sample of patients to the mean of the second sample of patients.

• 2-sample z-test. There is no natural pairing between the two samples, so the researcher must use a proportions test.

Is the mean height of female college students greater than 5.5 feet?

• Paired t-test. Students heights can be measured against females of similar backgrounds.

• 1-sample t-test. Test whether the mean of a single sample is equal to the target value of 5.5 feet.

• 2-sample t-test. Test whether the heights of female college students is higher than their high school heights.

• Use a z-test by finding the mean height and standard deviation of the sample of college females' heights.

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.

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

• 1-sample t-test. Test whether the mean of randomly assigned pairs of female and male students is greater than the mean of the average of males and females.

• z-test. Use proportions in place of means to run a one sample z-test for males and females and compare averages.

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.

• Accept the null hypothesis. There is 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.

The smaller the p-value, the stronger the evidence against the _____________ hypothesis

• null
• alternative