STAT 7.1-5

The local ranger station tracked and tagged 2,844 adult female black bears in a national park. A random sample of 9 adult female black bears from those tagged had an average body weight of 203 pounds with standard deviation 25 pounds. Which of the following is a point estimate for the population mean weight of all female black bears that are tagged?

• 9

• 25

• 203

• 2844

• 25/3

Researchers for a company that manufactures batteries want to test the hypothesis that the mean battery life of their new battery is greater than the known mean battery life of their older version. The researchers selected random samples of 32 of the new batteries, subjected the batteries to continuous use, and determined the mean and standard deviation of the battery lives in the sample.

Which of the following is an appropriate test for the researchers’ hypothesis?

• A one-sample z-test for a population mean

• A one-sample t-test for a population mean

• A one-sample z-test for a population proportion

• A matched-pairs t-test for a mean difference

• A two-sample t-test for a difference between means

Researchers at a medical center studied the amount of caffeine, in milligrams (mg), contained in a 16-ounce cup of coffee made at one machine at the center’s cafeteria. They selected a random sample of 40 16-ounce cups of coffee made at different times of the day during a one-month period. The mean and standard deviation of the amount of caffeine in the sample were 159.88 mg and 36.72 mg, respectively. A graph of the sample data revealed a right skew with one outlier. The researchers will construct a confidence interval to estimate the amount of caffeine for all 16-ounce cups made at the machine.

Which of the following conditions is not needed for the inference?

• The samples were selected at random.

• The observations are independent of one another.

• The sample size of 40 is less than 10% of the population size.

• The graph of the sample data is symmetric with no outliers.

• The sample size is large enough to assume that the sampling distribution of sample means is approximately normal.

For a certain brand of canned corn, the company claims that the mean weight of the contents of the cans is 15.25 ounces. A random sample of 36 cans were selected. The sample was found to have mean 15.18 ounces and standard deviation 0.12 ounce. A hypothesis test will be conducted to investigate whether there is evidence to support the belief that the mean is less than 15.25 ounces.

Which of the following is the correct test statistic for the hypothesis test?

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A random sample of 10 employees of a company was selected to estimate the mean one-way commute time for all employees at the company. The mean and standard deviation of the sample were 38 minutes and 6 minutes, respectively.

Assuming all conditions for inference are met, which of the following is the margin of error, in minutes, for a 95 percent confidence interval for the population mean one-way commute time?

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Which of the following correctly compares the t-distribution and z-distribution?

• For small sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric.

• For large sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric.

• The curves of both distributions are symmetric, but the height of the density curve of the t-distribution is taller than the height of the density curve of the z-distribution.

• The area under the density curve of the t-distribution is greater than the area under the density curve of the z-distribution, especially for small sample sizes.

• The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.

A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.

Which of the following is an appropriate method for the biologist to use for inference to the populationt

• A one-sample t-interval for a population mean

• A one-sample t-interval for a sample mean

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

• A matched-pairs t-interval for a mean difference

• A two-sample t-interval for a difference between means

A magazine article reported that college students spend an average of $100 on a first date. A university sociologist believed that number was too high for the students at the university. The sociologist surveyed 32 randomly selected students from the university and obtained a sample mean of $92.23 for the most recent first dates. A one-sample t-test resulted in a p-value of 0.026.

Which of the following is a correct interpretation of the p-value?

• The probability is 0.026 that the mean amount of money students from the university spend on a first date is less than $100.

• The probability is 0.026 that the mean amount of money students from the university spend on a first date is less than $92.23.

• The probability is 0.026 that the mean amount of money students from the university spend on a first date is more than $92.23.

• If the mean amount of money that students from the university spend on a first date is $100, the probability is 0.026 that a randomly selected group of 32 students from the university would spend a mean of $92.23 or less on their most recent first dates.

• If the mean amount of money that students from the university spend on a first date is less than $100, the probability is 0.026 that a randomly selected group of 32 students from the university would spend a mean of $92.23 or less on their most recent first dates.

A fast-food restaurant claims that a small order of french fries contains 120 calories. A nutritionist is concerned that the true average calorie count is higher than that. The nutritionist randomly selects 35 small orders of french fries and determines their calories. The resulting sample mean is 155.6 calories, and the p-value for the hypothesis test is 0.00093.

Which of the following is a correct interpretation of the p-value?

• If the population mean is 120 calories, the p-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or more.

• If the population mean is 120 calories, the p-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or less.

• If the population mean is 120 calories, the p-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or more, or a sample mean of 84.4 calories or less

• If the population mean is 155.6 calories, the p-value of 0.00093 is the probability of observing a sample mean of 120 calories or more.

• If the population mean is 155.6 calories, the p-value of 0.00093 is the probability of observing a sample mean of 120 calories or less.

A century ago, the average height of adult women in the United States was 63 inches. Researchers believe that the average might be greater today. A random sample of 40 adult women was selected from the population. The sample had mean 64.2 inches and standard deviation 2.9 inches. Assuming all conditions for inference are met, the researchers will perform an appropriate hypothesis test to investigate their belief.

Which of the following is the correct test statistic for the hypothesis test?

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