Chapter 10 Comparing Two Populations or groups

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.

Tags

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.

A quiz question gives random samples of n = 10 observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for the difference in the two population means. Janelle uses her calculator’s two-sample t interval with 16.87 degrees of freedom to compute the 95% confidence interval. Assume that both students calculate the intervals correctly.Which of the following is true?

• Tom’s confidence interval is wider.
• Janelle’s confidence interval is wider.
• Both confidence intervals are the same.
• There is insufficient information to determine which confidence interval is wider.

The P-value for the test is 0.048. A correct conclusionis to

• fail to reject H0 at the a = 0.05 level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
• fail to reject H0 at the a = 0.05 level. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
• reject H0 at the a = 0.05 level. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
• reject H0 at the a = 0.05 level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

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.

An SRS of size 100 is taken from Population A with proportion 0.8 of successes. An independent SRS of size 400 is taken from Population B with proportion 0.5 of successes. The sampling distribution for the difference (Population A –Population B) in sample proportions has what mean and standard deviation?

• mean = 0.3; standard deviation = 1.3
• mean = 0.3; standard deviation = 0.40
• mean = 0.3; standard deviation = 0.047
• mean = 0.3; standard deviation = 0.0022

How much more effective is exercise and drug treatment than drug treatment alone at reducing the rateof heart attacks among men aged 65 and older? Tofind out, researchers perform a completely randomized experiment involving 1000 healthy males inthis age group. Half of the subjects are assigned toreceive drug treatment only, while the other half are assigned to exercise regularly and to receive drug treatment. The most appropriate inference method for answering the original research question is

• one-sample z test for a proportion.
• two-sample z interval for p1 − p2.
• two-sample z test for p1 − p2.
• two-sample t interval for m1 − m2.

Tags

CCSS.HSS.IC.B.4

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.

In a simple random sample of 100 households in 2000, 43 had some credit card debt.  In another simple random sample of  150 households in 2012, 72 had some credit card debt.  Which of the following is the correct test statistic for testing the hypothesis , that there is no difference in the proportion of households with credit card debt in these two years?

• A
• B
• C

Choose the correct response

• Gives z = 2.25, P < 0.02
• Gives z = 2.60, P < 0.005
• Gives z = 2.25, P < 0.04
• Should not be used because the Normal Condition is violated