AP Statistics - MCQ Review #5

1. Monthly rent was determined for each apartment in a random sample of 100 apartments. The sample mean was $820 and the sample standard deviation was $25. An approximate 95 percent confidence interval for the true mean monthly rent for the population of apartments from which this sample was selected is ($815, $825). Which of the following statements is a correct interpretation of the 95 percent confidence level?

• 1. In this population, about 95 percent of all rental prices are between $815 and $825.

• In this sample, about 95 percent of the 100 rental prices are between $815 and $825.

• In repeated sampling, the method produces intervals that include the population mean approximately 95 percent of the time.

• In repeated sampling, the method produces intervals that include the sample mean approximately 95 percent of the time.

• There is a probability of 0.95 that the true mean is between $815 and $825.

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When using a one-sample t-procedure to construct a confidence interval for the mean of a finite population, a condition is that the population size be at least 10 times the sample size. The reason for the condition is to ensure that

• The sample size is large enough

• The central limit theorem is applicable for the sample mean

• The sample standard deviation is a good approximation of the population standard deviation

• The degree of dependence among observations is negligible

• The sampling method is not biased

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1. An experiment will be conducted to test the effectiveness of a weight-loss supplement. Volunteers will be randomly assigned to take either the supplement or a placebo for 90 days, with 12 volunteers in each group. The subjects will not know which treatment they receive. At the end of the experiment, researchers plan to calculate the mean weight loss for each of the two groups and to construct a two-sample t-confidence interval for the difference of the two treatment means. Which of the following assumptions is necessary for the confidence interval to be valid?

• The sample size is greater than or equal to 10 percent of the population size.

• Each of the two groups has at least 5 successes and at least 5 failures.

• The distributions of weight loss of the two treatments are approximately normally distributed.

• The volunteers in the supplement group are paired with volunteers in the placebo group.

• The expected number of people who lose weight in each group is at least 5.

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A large-sample 98 percent confidence interval for the proportion of hotel reservations that are canceled on the intended arrival day is (0.048, 0.112). What is the point estimate for the proportion of hotel reservations that are canceled on the intended arrival day from which this interval was constructed?

• 0.032

• 0.064

• 0.080

• 0.160

• It cannot be determined from the information given.

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A random sample of 432 voters revealed that 100 are in favor of a certain bond issue. A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is

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A test engineer wants to estimate the mean gas mileage, μ, (in miles per gallon) for a particular model of automobile. Eleven of these cars are subjected to a road test, and the gas mileage is computed for each car. A dotplot of the 11 gas-mileage values is roughly symmetrical and has no outliers. The mean and standard deviation of these values are 25.5 and 3.01, respectively. Assuming that these 11 automobiles can be considered a simple random sample of cars of this model, which of the following is the correct 95% confidence interval for the mean gas mileage?

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1. Popular wisdom is that eating presweetened cereal tends to increase the number of dental caries (cavities) in children. A sample of children was (with parental consent) entered into a study and followed for several years. Each child was classified as a sweetened-cereal lover or an unsweetened cereal lover. At the end of the study, the amount of tooth damage was measured. Pictured are the summary data:

Assuming the necessary conditions for inference are met, which of the following is an approximate 95% confidence interval for the difference in the mean tooth damage?

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Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months. A random sample of children will be selected, and the age at which each child begins to walk will be recorded. A 99 percent confidence interval for the average age at which children begin to walk will be constructed using the data obtained from the sample of children. Of the following, which is the smallest sample size that will result in a margin of error of 0.1 month or less for the confidence interval?

• 400

• 900

• 1,300

• 1,600

• 2,100

1. In 2009 a survey of Internet usage found that 79 percent of adults age 18 years and older in the United States use the Internet. A broadband company believes that the percent is greater now that it was in 2009 and will conduct a survey. The company plans to construct a 98 percent confidence interval to estimate the current percent and wants the margin of error to be no more than 2.5 percentage points. Assuming that at least 79 percent of adults use the Internet, which of the following should be used to find the sample size (n) needed?

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Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. If the reported percent has a margin of error of 2.7 percentage points, which of the following is closest to the level of confidence?

• 80.0%

• 90.0%

• 95.0%

• 95.5%

• 99.0%

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