STATS 7.6-10 diff means

A sports equipment researcher investigated how different types of wood used to make baseball bats might affect batting. The researcher selected a sample of 80 batters from summer baseball leagues and randomly assigned the batters to one of two groups: the ash bat group or the maple bat group. The mean number of hits for each group was recorded at the end of the season, and the difference in the sample means was calculated.

Which of the following is the appropriate inference procedure for analyzing the results of the investigation?

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

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

• A matched pairs t-interval for a mean difference

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

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

A sociologist will conduct a two-sample t-test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor’s degrees and people with master’s degrees. From a random sample of 32 people with a bachelor’s degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 28 people with a master’s degree, the average salary was $58,000 with a standard deviation of $4,000.

With a null hypothesis of no difference in the means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (master’s degree minus bachelor’s degree) ?

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A two-sample t-test for a difference in means was conducted to investigate whether defensive players on a football team can bench-press more weight, on average, than offensive players. The conditions for inference were met, and the test produced a test statistic of t=1.083 and a p-value of 0.15.

Based on the p-value and a significance level of �=0.05, which of the following is the correct conclusion?

• Reject the null hypothesis because 0.15>0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• Reject the null hypothesis because 0.15>0.05. There is convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• Fail to reject the null hypothesis because 0.15>0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• Fail to reject the null hypothesis because 0.15>0.05. There is convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

• Fail to reject the null hypothesis because 0.15>0.05. There is convincing evidence that defensive players can bench-press the same amount of weight, on average, as offensive players.

To test the durability of cell phone screens, phones are dropped from a height of 1 meter until they break. A random sample of 40 phones was selected from each of two manufacturers. The phones in the samples were dropped until the screens broke. The difference in the mean number of drops was recorded and used to construct the 90 percent confidence interval (0.46,⁢1.82) to estimate the population difference in means.

Consider the sampling procedure taking place repeatedly. Each time samples are selected, the phones are dropped and the statistics are used to construct a 90 percent confidence interval for the difference in means. Which of the following statements is a correct interpretation of the intervals?

• Approximately 90 percent of the intervals will extend from 0.46 to 1.82.

• Approximately 90 percent of the intervals constructed will capture the difference in sample means.

• Approximately 90 percent of the intervals constructed will capture the difference in population means.

• Approximately 90 percent of the intervals constructed will capture at least one of the sample means.

• Approximately 90 percent of the intervals constructed will capture at least one of the population means.

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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Animal researchers studying cows and horses conducted a two-sample t-test for a difference in means to investigate whether grazing cows eat more grass, on average, than grazing horses. All conditions for inference were met, and the test produced a test statistic of t=1.664 and a p-value of 0.0487.

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

• The probability that cows eat more grass than horses, on average, is 0.0487.

• The probability that cows eat the same amount of grass as horses, on average, is 0.0487.

• Assuming that the mean amount of grass eaten by cows is greater than the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.

• Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.

• Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at least 1.664 is 0.0487.

A study was conducted to investigate whether the mean price of a dozen eggs was different for two different grocery stores, Store A and Store B, in a large city. A carton of one dozen eggs from each store was randomly selected for each of 35 weeks, for a total sample size of 35 cartons from each store. The mean price of the 35 cartons was recorded for each store. The difference in the mean carton price for the stores will be calculated.

Which of the following is the appropriate test for the study?

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

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

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

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

• A two-sample t-test for a difference between population proportions

An ecologist is examining whether the number of fish caught in a large river basin has changed since a fire burned some of the surrounding forested area and vegetation along the river. Data in the form of fishing reports was available for a five-year period before the fire. From a random sample of 195 fishing reports before the fire, the mean catch was 6.3 fish with a standard deviation of 1.6. In a random sample of 143 reports three years after the fire, the mean catch was 7.1 fish with a standard deviation of 2.1.

Which of the following represents the standard error of the difference in the mean number of fish caught before and after the fire?

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City health officials will conduct a two-sample t-test for a difference in means to investigate whether stray dogs in the city have more fleas, on average, than do stray cats. A random sample of 22 stray dogs had a mean of 120 fleas and a standard deviation of 20 fleas. A random sample of 15 stray cats had a mean of 100 fleas and a standard deviation of 30 fleas.

Assuming a null hypothesis of no difference, which of the following is a correct test statistic for the test?

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A two-sample t-test for a difference in means was conducted to investigate whether the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. With all conditions for inference met, the test produced a test statistic of t=−2.073 and a p-value of 0.042.

Based on the p-value and a significance level of alpha=0.05, which of the following is a correct conclusion?

• There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke.

• There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke

• There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is greater than the average time to swim a lap with the butterfly stroke.

• There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke.

• There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke.