AP stats reveiw part A

A one-sample z -test for a population proportion

A study reported that 28 percent of middle school students in a certain state participate in community service activities. A teacher believes that the rate is greater than 28 percent for the middle school students in the teacher's district. The teacher selected a random sample of middle school students from the district, and the percent of students in the sample who participated in community service activities was found to be 32 percent. Which of the following is the most appropriate method for investigating the teacher's belief?

A one-sample z -test for a population proportion

A study reports that 75 percent of young adults in a county get their news from online sources. A sociologist believes that the percentage is actually greater than 75 percent. The sociologist will select a random sample of young adults from around the county to interview. Which of the following is the most appropriate method for investigating the sociologist's belief?

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

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?

A one-sample z -interval for a population proportion

Biologists studying horseshoe crabs want to estimate the percent of crabs in a certain area that are longer than 35 centimeters. The biologists will select a random sample of crabs to measure. Which of the following is the most appropriate method to use for such an estimate?

Of all possible samples of the same size, 3.22% will result in a success rate of 93.6% or less.

Chicken hatcheries employ workers to determine the sex of the baby chicks. The hatcheries claim that the workers are correct 95 percent of the time. An investigator believes the workers' success rate (workers are correct) is actually less than 95 percent of the time. The investigator selects a random sample of chicks and finds that the hatchery workers had a success rate of 0.936. The conditions for inference were checked and verified, and the p�-value of the test was given as 0.0322. If the null hypothesis is true, which of the following statements is a correct interpretation of the p�-value?

the null hypothesis is true.

In a hypothesis test for a single proportion, which of the following is assumed for the calculation of the p-value?

At the significance level α=0.05�=0.05, the null hypothesis is rejected. There is convincing evidence to support the claim that fewer than 40% of the students at the local university read at least one book last year.

A book club wonders if fewer than 40 percent of students at a local university had read at least one book during the last year. To test the claim, the book club selected a random sample of students at the local university and recorded the number of students who had read at least one book during the last year. The club conducted a test with the hypotheses H0:p=0.40H0:�=0.40 versus Ha:p<0.40Ha:�<0.40. The test yielded a p�-value of 0.033. Assuming all conditions for inference were met, which of the following is an appropriate conclusion?

0.0122

A hypothesis test was conducted to investigate whether the population proportion of students at a certain college who went to the movie theater last weekend is greater than 0.2. A random sample of 100 students at this college resulted in a test statistic of 2.25. Assuming all conditions for inference were met, which of the following is closest to the p�-value of the test?

No, because the p�-value 0.053 is greater than the significance level 0.05. Answer A

A major credit card company is interested in the proportion of individuals who use a competitor's credit card. Their null hypothesis is H0: p=0.65H0: �=0.65, and based on a sample they find a sample proportion of 0.70 and a p�-value of 0.053. Is there convincing statistical evidence at the 0.05 level of significance that the true proportion of individuals who use the competitor's card is actually greater than 0.65 ?

No, because the sample may not be representative of all people in the state.

A marketing representative wants to estimate the proportion of people in a state who like the new design on the packaging of a certain cleaning product. The representative interviewed 100 people at a certain supermarket, and 82 people indicated that they liked the new design. Have the conditions for creating a confidence interval for the population proportion been met?

The expected number of teens in the sample who do not use social media is less than 10.

A newspaper article claims that 92 percent of teens use social media. To investigate the claim, a polling organization selected a random sample of 100 teens, and 96 teens in the sample indicated that they use social media. Given the data, why is it not appropriate to use a one-sample z�-test for a proportion to test the newspaper's claim?

The random sample condition (II) is a check for independence, not normality. Also, the sample size in relation to the population size condition (IIIIII) is a check for independence, not normality.

A one-sample z�-test for a population proportion p� will be conducted. Which of the following conditions checks that the sampling distribution of the sample proportion is approximately normal? The sample is selected at random. np0≥10��0≥10 and n(1−p0)≥10�(1−�0)≥10 for sample size n�. The sample size is less than or equal to 10 percent of the population size. A II only

A one-sample z -interval for a population

A random sample of 500 adults living in a large county was selected and 304 adults from the sample indicated that the unemployment rate was of great concern. What is the standard error of the sample proportion pˆ

We are 95 percent confident that the proportion of all residents in the town who favor the proposal is between 0.361 and 0.579.

A random sample of 83 residents of a certain town were asked whether they approve of a proposal to improve the town's aging bridges. The 95 percent confidence interval to estimate the proportion of all residents of the town who approve of the proposal was calculated to be (0.361,0.579) . Which of the following is a correct interpretation of the interval?

Less than 80 percent of all people in the country try to include locally grown foods in their diets.

A recent national survey indicated that 73 percent of respondents try to include locally grown foods in their diets. A 95 percent confidence interval for the proportion of all people in the country who try to include locally grown foods in their diets is given as (0.70,0.76) . Assume all conditions for inference were met. Based on the confidence interval, which of the following claims is supported?

More than half of all people prefer texting.

A recent survey of cell phone users indicated that 56 percent of the respondents prefer to use cell phones for texting rather than for making phone calls. A 95 percent confidence interval for the estimate of all cell phone users who prefer to use cell phones for texting has a margin of error of 3 percent. Assume all conditions for inference have been met. Based on the confidence interval, which of the following claims is supported?

The square root of the .36 and .64 over 150

In the United States, 36 percent of the people have a blood type that is A positive. From a random sample of 150 people from Norway, 66 had a blood type that was A positive. Consider a hypothesis test to investigate whether the proportion of people in Norway with a blood type of A positive is different from that in the United States. Which of the following is the standard deviation used to calculate the test statistic for the one-sample z-test?

No, the significance level is the probability of rejecting the null hypothesis when the null hypothesis is actually true.

Is the significance level of a hypothesis test equivalent to the probability that the null hypothesis is true?

If the population proportion is 0.80, the probability of observing a sample proportion of at least 0.84 or at most 0.76 is 0.273.

Molly works for a meat producer, and she needs to determine whether containers of ground beef have the correct fat content. She obtains a random sample of 120 containers of ground beef and finds that 84 percent have the correct fat content. Molly then conducts a hypothesis test of H0:p=0.80H0:�=0.80 versus Ha:p≠0.80Ha:�≠0.80 and calculates a test statistic of 1.10 with a p�-value of 0.273. Which of the following best represents the meaning of the p�-value?

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

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?

8 percent

Suppose a 90 percent confidence interval to estimate a population proportion was calculated from a sample proportion of 18 percent and a margin of error of 4 percent. What is the width of the confidence interval?

The probability that p is in the interval is equal to the level of confidence for the interval.

Suppose a researcher wants to use a confidence interval to estimate an unknown population proportion p p . Which of the following is not a correct statement?

A one-sample z -interval for a population proportion

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?