Inferences for Means

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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Animal scientists studied foraging behavior of the scrub lizard, found in central Florida. Foraging is the process of searching for food. To study such behavior, the scientists recorded the number of head movements per minute for a sample of 63 lizards. A 95 percent confidence interval constructed from the sample is given as 2.7±0.62

head movements per minute. Based on the interval, is a claim of 3 head movements per minute plausible?

• The claim is not plausible because 3 head movements per minute is contained within the interval.

• The claim is not plausible because 3 head movements per minute is not contained within the interval.

• The claim is not plausible because 95 percent of 3 is greater than the sample mean of 2.7.

• The claim is plausible because 3 head movements per minute is not contained within the interval.

• The claim is plausible because 3 head movements per minute is contained within the interval.

To test the effectiveness of an exercise program in reducing high blood pressure, 15 participants had their blood pressures recorded before beginning the program and again after completing the program. The difference (after minus before) in blood pressure was recorded for each participant, and the sample mean difference was calculated. A hypothesis test will be conducted to investigate whether there is convincing statistical evidence for a reduction in blood pressure for all who complete the program.Which of the following is the correct set of hypotheses?

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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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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 national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58.

Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?

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A consumer group studied two different manufacturers of cars, J and K, to investigate differences in gas mileage for cars made by the two manufacturers. For a similar type of car, a random sample of 15 cars from J and a random sample of 12 cars from K were selected, and the gas mileages, in miles per gallon (mpg), were recorded. The difference in the sample mean gas mileages was used to construct the 90 percent confidence interval (3.5,5.7). Assuming all conditions for inference were met, which of the following is a correct interpretation of the interval?

• The probability is 0.90 that the difference in sample means for gas mileage for the two car manufacturers is between 3.5 mpg

  and 5.7 mpg

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• The probability is 0.90 that the population mean difference in gas mileage for the two car manufacturers is between 3.5 mpg

  and 5.7 mpg

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• About 90 percent of the differences in gas mileage for the two car manufacturers are between 3.5 mpg and 5.7 mpg

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• We are 90 percent confident that the difference in sample means for gas mileage for the two car manufacturers is between 3.5 mpg and 5.7 mpg

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• We are 90 percent confident that the population mean difference of gas mileage for the two car manufacturers is between 3.5 mpg and 5.7 mpg

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A reporter responsible for the food section of a magazine investigated the belief that grocery stores sell beef at a higher price in the fall than in the spring. The reporter selected independent random samples of grocery-store beef prices in November and April and computed the mean and standard deviation for the samples. Which of the following are the correct null and alternative hypotheses for the reporter’s investigation, where μF

represents the mean price of beef in the fall and μS

represents the mean price of beef in the spring?

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Researchers on car safety studied driver reaction time and cell phone use while driving. Participants in the study talked on either a hands-free phone or a handheld phone while driving in a car simulator. A two-sample t -test for a difference in means was conducted to investigate whether the mean driver reaction time between the two groups of participants was different. All conditions for inference were met, and the test produced a test statistic of t=−2.763 and a p-value of 0.03. Which of the following is a correct interpretation of the p

-value?

• Assuming that the mean reaction times for hands-free and handheld phones are equal, the probability of obtaining a test statistic less than −2.763

  is 0.03.

• Assuming that the mean reaction times for hands-free and handheld phones are equal, the probability of obtaining a test statistic greater than 2.763 or less than −2.763

  is 0.03.

• Assuming that the mean reaction times for hands-free and handheld phones are not equal, the probability of obtaining a test statistic less than −2.763

  is 0.03.

• Assuming that the mean reaction times for hands-free and handheld phones are not equal, the probability of obtaining a test statistic greater than 2.763 or less than −2.763

  is 0.03.

• The probability that the mean reaction time for hands-free phones will be less than that for handheld phones is 0.03.

What did the Texas Rangers win in 2023?

• The World Series

• The Sorld Weries

• The Sorld Series

• The World Wories