AP Statistics Spring Quiz 1 Chapter 9

The mean and standard deviation of a random sample of 7 baby orca whales were calculated as 430 pounds and 26.9 pounds, respectively. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the mean weight of all baby orca whales?

To estimate the average cost of flowers for summer weddings in a certain region, a journalist selected a random sample of 15 summer weddings that were held in the state. A graph of the sample data showed an approximately symmetric distribution with no outliers. The sample mean and standard deviation were $734 and $102, respectively. The journalist will create a 95 percent confidence interval to estimate the population mean. Have all conditions for inference been met?

• No, because the graphical display is approximately symmetric it cannot be assumed that the sampling distribution of sample means is approximately normal.

• No, the sample size of 15 is not less than 10 percent of all weddings in the state.

• No, the 15 weddings in the sample were not selected at random.

• Yes, all conditions have been met.

• No, the sample size is not large enough to assume the sampling distribution of sample means is approximately normal.

Researchers studying the sticky droplets found on spider webs will measure the widths of a random sample of droplets. From the sample, the researchers will construct a 95 percent confidence interval to estimate the mean width of all such droplets. Which of the following statements about a 95 percent confidence interval for the mean width is correct?

• The width of the interval will not be affected if the researchers increase or decrease the number of droplets in the sample.

• The interval will be narrower if the researchers increase the level of confidence to 99 percent.

• The interval will be wider if the researchers decrease the level of confidence to 90 percent.

• The interval will be narrower if the researchers increase the sample size of droplets.

• The interval will be wider if the researchers increase the sample size of droplets.

A linguist at a large university was studying the word length of papers submitted by students enrolled in humanities programs. From a random sample of 25 papers, the linguist counted the number of words used in each paper. The 95 percent confidence interval was calculated to be (20,995, 22,905). Which of the following statements is correct?

• The probability is 0.95 that the mean word length for all papers submitted by students in humanities programs is between 20,995 words and 22,905 words.

• For all students in humanities programs who submit papers, 95 percent of the papers are between 20,995 words and 22,905 words.

• We are 95 percent confident that the mean word length for the papers submitted by students in the sample is between 20,995 words and 22,905 words.

• We are 95 percent confident that the mean word length for all papers submitted by students in humanities programs is between 20,995 words and 22,905 words.

• The probability is 0.95 that the mean word length for the papers submitted by students in the sample is between 20,995 words and 22,905 words.

A certain ambulance service wants its average time to transport a patient to the hospital to be 10 minutes. A random sample of 12 transports yielded a 95 percent confidence interval of 11.8±1.6 minutes. Is the claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital plausible based on the interval?

• The claim is not plausible because 10 falls outside of the interval.

• The claim is plausible because 10 falls within the interval.

• The claim is not plausible because 10 falls within the interval.

• The claim is plausible because 10 falls within 0.95 units of the interval.

• The claim is plausible because 10 falls outside of the interval.

The manager of a city recreation center wants to estimate the percent of city residents who favor a proposal to build a new dog park. To gather data, the manager will select a random sample of city residents. Which of the following is the most appropriate interval for the manager to use for such an estimate?

• A two-sample z -interval for a difference between population proportions.

• A one-sample z -interval for a sample proportion.

• A one-sample z -interval for a difference between population proportions.

• A one-sample z -interval for a population proportion.

• A two-sample z -interval for a difference between sample proportions.

Leslie is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month?

A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town library. A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?

• No, because the sample is not large enough to satisfy the normality conditions.

• No, because the size of the population is not known.

• Yes, because the sample is large enough to satisfy the normality conditions.

• Yes, because the sample was selected at random.

• Yes, because sampling distributions of proportions are modeled with a normal model.

Sue and Javier are working on a statistics project to estimate the proportion of students at their school who have a pet dog. Sue selects a random sample of 81 students from the 2,400 students at their school, and Javier selects a separate random sample of 64 students. They will both construct a 90 percent confidence interval from their estimates. Consider the situation in which the sample proportion from Sue’s sample is equal to the sample proportion from Javier’s sample. Which of the following statements correctly describes their intervals?

• Javier’s interval will have a greater degree of confidence than Sue’s interval will.

• Sue’s interval will have a greater degree of confidence than Javier’s interval will.

• The width of Sue’s interval will be narrower than the width of Javier’s interval.

• The width of Sue’s interval will be the same as the width of Javier’s interval.

• The width of Sue’s interval will be wider than the width of Javier’s interval.