Unit 7 Day 5 ET

Honor Code.

• True

• False

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 5% , which of the following is the correct conclusion?

 

• A) 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.

• B) 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.

• C) 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.

• D) 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.

• E) 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.

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?

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

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

• C) 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.

• D) 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.

• E) 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 team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use?

 

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

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

• C) A one-sample t-interval for a population proportion

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

• E) A two-sample t-interval for a difference between proportions

The director of fitness for a large corporation with over 5,000 employees recorded the resting heart rate, in beats per minute (bpm) , for 35 employees who were known to wear activity trackers. The following boxplot summarizes the result.

 

The director wants to estimate the resting heart rate for all employees with a confidence interval. Have all conditions for inference been met?

• A) Yes, all conditions have been met.

• B) No, the distribution of the sample data is not approximately symmetric.

• C) No, the sample size is greater than 10 percent of the population size.

• D) No, the distribution of resting heart rate in the population cannot be assumed to be approximately normal.

• E) No, the sample was not selected at random

Researchers investigated whether there is a difference between two headache medications, R and S. Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication.

Have the conditions been met for inference with a confidence interval for the difference in population means?

• A) Yes, all conditions have been met.

• B) No, because the data were not collected using a random sample.

• C) No, because cause and effect cannot be inferred since there is a random sample.

• D) No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal.

• E) No, because the sample sizes are not the same.

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?

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

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

   

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

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

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

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  represents the mean price of beef in the fall and  represents the mean price of beef in the spring?

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

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

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

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

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