Chapter 10 MC (No Paired)

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?

• Yes; we have two independent random samples and large sample sizes.

• No; road rage scores on a scale from 0 to 20 can't be Normal.

• Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.

• No; we don't know the population standard deviations.

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.

Which of the following is a 95% 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?

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Tags

CCSS.HSS.IC.B.4

The power takeoff driveline on tractors used in agriculture can be a serious hazard to operators of farm equipment. The driveline is covered by a shield in new tractors, but 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 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.

• The counts of successes and failures are large enough to use Normal calculations.

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  Both populations are more than 10 times the corresponding sample sizes.

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 width.

• 
  Janelle made a mistake; degrees of freedom has to be a whole number.

Tags

CCSS.HSS.IC.B.4

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of 𝐻0:𝜇𝑠𝑢𝑏𝑢𝑟𝑏𝑎𝑛=𝜇𝑐𝑖𝑡𝑦 versus a two-sided alternative.

Which is the correct standardized test statistic?

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Tags

CCSS.HSS.ID.A.4

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of 𝐻0:𝜇𝑠𝑢𝑏𝑢𝑟𝑏𝑎𝑛=𝜇𝑐𝑖𝑡𝑦 versus a two-sided alternative.

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

• reject 𝐻0 because 0.048<𝛼=0.05. 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 because 0.048<𝛼=0.05. 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 because 0.048<𝛼=0.050. 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.

• fail to reject 𝐻0 because 0.048<𝛼=0.050. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

Tags

CCSS.HSS.IC.B.4

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 (Game – Concert) in population proportions 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 cannot conclude that the proportion of iPod owners at the two venues is different.

• 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 can conclude that the proportion of iPod owners at the two venues is the same.

• 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.

Tags

CCSS.HSS.IC.B.4

Researchers want to evaluate the effect of a natural product on reducing blood pressure. They plan to carry out a randomized experiment to compare the mean reduction in blood pressure of a treatment (natural product) group and a placebo group. Then they will use the data to perform a test of 𝐻0:𝜇𝑇−𝜇𝑃=0 versus 𝐻𝑎:𝜇𝑇−𝜇𝑃>0, where 𝜇𝑇= the true mean reduction in blood pressure when taking the natural product and 𝜇𝑃= the true mean reduction in blood pressure when taking a placebo for subjects like the ones in the experiment. The researchers would like 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 test using 𝛼 = 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 to detect a 5-point difference instead, then the power of the test

• would be less than 80%.

• would be greater than 80%.

• would vary depending on the standard deviation of the data.

• 
  

  could be either less than or greater than 80%.