Name:    AP Statistics Chapter 10 Test - Comparing Two Populations or Groups

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Suppose we have two SRSs from two distinct populations and the samples are independent.  We measure the same variable for both samples.  Suppose both populations of the values of these variables are Normally distributed but the population means and standard deviations are unknown.  For purposes of comparing the two means, we use
 A) Two-sample t procedures B) Matched pairs t procedures C) Two-proportion z procedures D) The least-squares regression line E) None of the above.

2.

We wish to test if a new feed increases the mean weight gain compared to an old feed. At the conclusion of the experiment it was found that the new feed gave a 10 kg bigger gain than the old feed. A two-sample t test with the proper one-sided alternative was done and the resulting P-value was 0.082. This means that
 A) there is an 8.2% chance the null hypothesis is true. B) there was only an 8.2% chance of observing an increase greater than 10 kg (assuming the null hypothesis was true). C) there was only an 8.2% chance of observing an increase greater than 10 kg (assuming the null hypothesis was false). D) there is an 8.2% chance the alternative hypothesis is true. E) there is only an 8.2% chance of getting a 10 kg increase.

3.

A study was conducted to investigate the effectiveness of a new drug for treating Stage 4 AIDS patients. A group of AIDS patients was randomly divided into two groups. One group received the new drug; the other group received a placebo. The difference in mean subsequent survival (those with drugs – those without drugs) was found to be 1.04 years, and a 95% confidence interval was found to be 1.04 ± 2.37 years. Based upon this information, we can conclude that
 A) the drug was effective since those taking the drug lived, on average, 1.04 years longer. B) the drug was ineffective since those taking the drug lived, on average, 1.04 years less. C) there is no evidence the drug was effective since the 95% confidence interval covers zero. D) there is evidence the drug was effective since the 95% confidence interval does not cover zero. E) we can make no conclusions since we do not know the sample size or the actual mean survival of each group.

4.

Different varieties of fruits and vegetables have different amounts of nutrients. These differences are important when these products are used to make baby food. We wish to compare the carbohydrate content of two varieties of peaches. Specifically, we wish to test if the two varieties are significantly different in their mean carbohydrate content. The null and alternative hypotheses are
 A) B) C) D) E)

5.

Thirty-five people from a random sample of 125 workers from Company A admitted to using sick leave when they weren’t really ill.  Seventeen employees from a random sample of 68 workers from Company B admitted that they had used sick leave when they weren’t ill.  A 90% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren’t ill is
 A) B) C) D) E)

6.

To use the two-sample t procedure to perform a significance test on the difference between two means, we assume that
 A) the populations’ standard deviations are known. B) the samples from each population are independent. C) the distributions are exactly Normal in each population. D) the sample sizes are large. E) all of the above

7.

In a large midwestern university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1993 found that 20 finished in the bottom third of their high school class.  Admission standards at the university were tightened in 1995. In 1997 an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class.  Let p1 and p2 be the proportion of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom third of their high school class. What conclusion should we draw?
 A) We are 95% confident that the admissions standards have been tightened. B) Reject H0 at the = 0.01 significance level. C) Fail to reject H0 at the = 0.05 significance level. D) There is significant evidence at the 5% level of a decrease in the proportion of freshmen who graduated in the bottom third of their high school class that were admitted by the university. E) If we reject H0 at the = 0.05 significance level based on these results, we have a 5% chance of being wrong.

8.

42 of 65 randomly selected people at a baseball game report owning an iPod.  34 of 52 randomly selected people at a rock concert occurring at the same time across town reported owning an iPod.  A researcher wants to test the claim that the proportion of iPod owners at the two venues is not the same.  A 90% confidence interval for the difference in population proportions is .  Which of the following gives the correct outcome of the researchers’ test of the claim?
 A) Since the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same. B) Since the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues may be the same. C) Since the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is different. D) Since the confidence interval includes more positive than negative values, we can conclude that a higher proportion of people at the baseball game own iPods than at the rock concert. E) We cannot draw a conclusion about a claim without performing a significance test.

9.

The power takeoff driveline on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The driveline 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, a sample of older tractors with both types of shields was taken to see what proportion 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 test the hypothesis H0: pb = pvs. Ha: pbpf where pb and pf are the proportion of tractors with the bolt-on and flip-up shields removed, respectively.  Which of the following conditions for performing the appropriate significance test is satisfied in this case?
 A) Both population distributions are Normally distributed. B) Two independent simple random samples were chosen. C) Both sample sizes are at least 30. D) np and n(1 – p) are both large enough to use Normal calculations. E) The sample size is at least 10 times the population size.

10.

All of us nonsmokers can rejoice—the mosaic tobacco virus that affects and injures tobacco plants is spreading! Meanwhile, a tobacco company is investigating if a new treatment is effective in reducing the damage caused by the virus. Eleven plants were randomly chosen. On each plant, one leaf was randomly selected, and one half of the leaf (randomly chosen) was coated with the treatment, while the other half was left untouched (control). After two weeks, the amount of damage to each half of the leaf was assessed.

What is the best reason for performing a paired experiment rather than a two–independent sample experiment in this case?
 A) It is easier to do since we need fewer experimental units and each unit receives more than one treatment. B) It allows us to remove variation in the results caused by other factors since we can compare both treatments within the same experimental unit. C) The computer program is more accurate since we work only with the differences. D) It requires fewer assumptions since we are interested only in the difference between treatments. E) It allows us to do more experiments since we use each experimental unit twice.