Chapter 15 Quiz

The distribution of actual weights of 8‑ounce wedges of cheddar cheese produced at a dairy is Normal, with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. What is the standard deviation of the sampling distribution of the mean? 0.0633 ounces 0.963 ounces 0.075 ounces 0.315 ounces

0.0633 ounces

A carpet manufacturer is inspecting for flaws in the finished product. If there are too many blemishes, the carpet will have to be destroyed. He finds the number of flaws in each square yard and is interested in the average number of flaws per 10 square yards of material. If we assume the standard deviation of the number of flaws per square yard is 0.6, the sample mean, 𝑥¯ , for the 10 square yards will have what standard deviation? Round the answer to the nearest hundredth. 0.19 0.06 0.60

0.19

The number of years of education of self‑employed individuals in the United States has a population mean of 13.6 years and a population standard deviation of 3 years. If we survey a random sample of 100 self‑employed people to determine the average number of years of education for the sample, what is the standard deviation of the sampling distribution of 𝑥¯, the sample mean? 3 years 0.3 years 13.6 years

0.3 years

The number of years of education of self‑employed individuals in the United States has a population mean of 13.6 years and a population standard deviation of 3 years. If we survey a random sample of 100 self‑employed people to determine the average number of years of education for the sample, what is the mean of the sampling distribution of 𝑥¯, the sample mean? 13.6 years 3 years 0.3 years

13.6 years

At a certain driver's license testing station,only 40% of all new drivers pass the behind‑the‑wheel test the first time they take it. A sample of 50 new drivers from a certain high school found that 36% of them had passed the test the first time. Which of these numbers is a statistic? 40% 36% 50

36%

At a certain driver's license testing station, only 40% of all new drivers pass the behind‑the‑wheel test the first time they take it. A sample of 50 new drivers from a certain high school found that 36% of them had passed the test the first time. Which of these numbers is a parameter? 36% 40% 50

40%

The distribution of actual weights of 8‑ounce wedges of cheddar cheese produced at a dairy is Normal, with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. The distribution of the sample mean of the weights of cheese wedges is: approximately Normal, with mean 8.1 and standard deviation 0.063. impossible to determine, because the sample size is too small. approximately Normal, with mean 8.1 and standard deviation 0.020. approximately Normal, with mean 8.1 and standard deviation 0.2.

Approximately Normal, with mean 8.1 and a SD of 0.063

In the 2000 presidential election, three candidates split the vote as follows. Bush 47.9% Gore 48.4% Nader 2.7% We will consider a vote for Al Gore a "success." We can look back and select a random sample of 50 voters from the 2000 election, and count the number of those who voted for Gore. Suppose, in that sample, that 23 of the 50 (46%) voted for Gore. Which of the following is correct? The numbers 50 and 23 are statistics, and the number 0.484 is a parameter. The numbers 23 and 0.46 are statistics, and the number 0.484 is a parameter. The numbers 0.46 and 0.484 are statistics.

The numbers 23 and 0.46 are statistics and the number 0.484 is a parameter.

Suppose that two very large companies, A and B, each select random samples of their employees. Company A has 5,000 employees and Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee. If each firm randomly selects 3% of its employees, which statement is true about the sampling distributions of the sample means? The smaller company, Company A, will have a sampling distribution with smaller standard deviation. The sampling distributions of the sample means will have about the same standard deviation because, in both cases, we're selecting 3% of the employees. None of the answer options are correct. The standard deviation of the sampling distribution of the sample mean will be smaller for the larger company, Company B, because a larger sample is being selected.

The standard deviation of the sampling distribution of the sample mean will be smaller for the larger company, Company B, because a larger sample is being selected.

The Department of Motor Vehicles reports that 32% of all vehicles registered in a state are made by a Japanese or a European automaker. The number 32% is best described as: a parameter. a statistic. a sample proportion.

a parameter

For which of the following situations would the central limit theorem not imply that the sample distribution for 𝑥¯ is approximately Normal? a population is Normal, and we use samples of size 𝑛=6 . a population is not Normal, and we use samples of size 𝑛=6 . a population is Normal, and we use samples of size 𝑛=50 . a population is not Normal, and we use samples of size 𝑛=50

a population is not Normal, and we use samples of size n=6

In a large population of college‑educated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign. The distribution of the sample mean IQ is: approximately Normal, with mean 112 and standard deviation 0.083. approximately Normal, with mean 112 and standard deviation 1.443. approximately Normal, with mean 112 and standard deviation 25. approximately Normal, with mean equal to the observed value of the sample mean and standard deviation 25.

approximately Normal, with mean 112 and standard deviation 1.443.

A simple random sample of 1000 American adults found that the average number of hours spent watching television during a typical week was 13.8. A simple random sample of 500 Canadians yielded an average of 12.5 hours per week of television viewing. Assume that for the American and Canadian distributions for weekly television, viewing times have the same standard deviations. The sampling variability associated with these sample means is: larger for the sample of Canadians, because Canadian citizens are more widely dispersed throughout their country than American citizens are in the United States. Hence, Canadians have more variable views. larger for the sample of Canadians, because the sample size is smaller. smaller for the sample of Canadians, because the population of Canada is less than half that of the United States. smaller for the sample of Canadians, because their population is smaller.

larger for the sample of Canadians, because the sample size is smaller.

The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age 𝑥¯ of these residents is to be computed. We know the random variable 𝑥¯ has approximately a Normal distribution because: the population from which we're sampling has a Normal distribution. of the central limit theorem. of the 68‑95‑99.7 rule. of the law of large numbers.

of the central limit theorem

Suppose you interview 10 randomly selected workers and ask how many miles they commute to work. You'll compute the sample mean commute distance. Now imagine repeating the survey many, many times, each time recording a different sample mean commute distance. In the long run, a histogram of these sample means represents: the sampling distribution of the sample mean. the true population average commute distance. the bias, if any, that is present in the sampling method. a simple random sample.

the sampling distribution of the sample mean