Stats Chapter 7 Review

Suppose we select an SRS of size n = 100 from a large population having proportion p of successes. Let p^ be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p^ ? (a) 0.01 (b) 0.09 (c) 0.85 (d) 0.975 (e) 0.999

(c) 0.85

The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean (a) if the sample size is reasonably large (for any population). (b) if the population is Normally distributed and the sample size is reasonably large. (c) if the population is Normally distributed (for any sample size). (d) if the population is Normally distributed and the population standard deviation is known (for any sample size). (e) if the population size is reasonably large (whether the population distribution is known or not).

(a) if the sample size is reasonably large (for any population).

A researcher initially plans to take an SRS of size n from a population that has mean 80 and standard deviation 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied by (a) √2. (b) 1/√2. (c) 2. (d) 1/2. (e) 1/√2n.

(b) 1/√2.

The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about 3% of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact,p = 0.80 at both schools. Which of the following is the best conclusion? (a) The estimate from Johns Hopkins has less sampling variability than that from Ohio State. (b) The estimate from Johns Hopkins has more sampling variability than that from Ohio State. (c) The two estimates have about the same amount of sampling variability. (d) It is impossible to make any statement about the sampling variability of the two estimates because the students surveyed were different. (e) None of the above.

(b) The estimate from Johns Hopkins has more sampling variability than that from Ohio State.

The student newspaper at a large university asks an SRS of 250 undergraduates, "Do you favor eliminat- ing the carnival from the term-end celebration?"All in all, 150 of the 250 are in favor. Suppose that (unknown to you) 55% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n = 250 from this popula- tion, the sampling distribution of the sample propor- tion p^ would be (a) exactly Normal with mean 0.55 and standard devia- tion 0.03. (b) approximately Normal with mean 0.55 and standard deviation 0.03. (c) exactly Normal with mean 0.60 and standard devia- tion 0.03. (d) approximately Normal with mean 0.60 and standard deviation 0.03. (e) heavily skewed with mean 0.55 and standard devia- tion 0.03.

(b) approximately Normal with mean 0.55 and standard deviation 0.03.

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working prop- erly, the amount poured into the bottles follows a Normal distribution with mean 16.05 ounces and standard deviation 0.1 ounce. Assume that the machine is working properly. If four bottles are randomly selected and the number of ounces in each bottle is measured, then there is about a 95% chance that the sample mean will fall in which of the following intervals? (a) 16.05 to 16.15 ounces (b) 16.00 to 16.10 ounces (c) 15.95 to 16.15 ounces (d) 15.90 to 16.20 ounces (e) 15.85 to 16.25 ounces

(c) 15.95 to 16.15 ounces

A study of voting chose 663 registered voters at ran- dom shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers? (a) 72% is a sample; 56% is a population. (b) 72% and 56% are both statistics. (c) 72% is a statistic and 56% is a parameter. (d) 72% is a parameter and 56% is a statistic. (e) 72% and 56% are both parameters.

(c) 72% is a statistic and 56% is a parameter.

The Gallup Poll has decided to increase thesize of its random sample of voters from about 1500 people to about 4000 people right beforean election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to (a) reduce the bias of the estimate. (b) increase the bias of the estimate. (c) reduce the variability of the estimate. (d) increase the variability of the estimate. (e) reduce the bias and variability of the estimate.

(c) reduce the variability of the estimate.

Which of the following statements about the sampling distribution of the sample mean is incorrect? (a) The standard deviation of the sampling distribution will decrease as the sample size increases. (b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples. (c) The sample mean is an unbiased estimator of the population mean. (d) The sampling distribution shows how the sample mean will vary in repeated samples. (e) The sampling distribution shows how the sample was distributed around the sample mean.

(e) The sampling distribution shows how the sample was distributed around the sample mean.

Suppose that you are a student aide in the library and agree to be paid according to the "random pay" system. Each week, the librar- ian flips a coin. If the coin comes up heads, your pay for the week is $80. If it comes up tails, your pay for the week is $40. You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x-. The shape of the sampling distribution of x will be (a) Normal. (b) approximately Normal. (c) right-skewed. (d) left-skewed. (e) symmetric but not Normal.

(e) symmetric but not Normal.