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?

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.

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.

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

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 proportions

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 different from 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 less 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 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.

A biologist studied the frequency of croaks for frogs from two different regions. From a random sample of 32 frogs located in the northern region, the mean number of croaks per hour was 21.3, and from a random sample of 38 frogs located in the southern region, the mean number of croaks per hour was 28.9. To estimate the difference in the mean number of croaks (southern minus northern), a 95 percent confidence interval was constructed from the samples. The interval was reported as (7.1,8.1). Which of the following claims is supported by the interval?

The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.

All southern frogs croak more times per hour than do all northern frogs.

The northern frogs are likely to have a greater mean number of croaks per hour than the southern frogs.

All frogs in the study have about the same number of croaks per hour.

The northern and southern frogs have the same mean number of croaks per hour.

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?

Yes, all conditions have been met.

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

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

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

No, because the sample sizes are not the same.

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 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 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 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.

Two 99 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and W. One confidence interval, i_9, will be constructed using samples of size 9 from each of R and W, and the other confidence interval, i_81, will be constructed using samples of size 81 from each of R and W. When all other things remain the same, which of the following describes the relationship between the two confidence intervals?

The width of i_81 will be 1/3 the width of i_9.

The width of i_81 will be 1/9 the width of i_9.

The width of i_81 will be equal to the width of i_9.

The width of i_81 will be 3 times the width of i_9.

The width of i_81 will be 9 times the width of i_9.

Estimating Differences Between Populations Using Samples Quiz

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

_______ is a part of a group being surveyed.

Sample

Population

Random Sample

Quartile

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

237 fifth graders and 346 fourth graders went on a field trip. Estimate how many more fourth graders were on a field trip than fifth graders.

200 more

109 more

100 more

110 more

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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?

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.

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.

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

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.

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.

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

You ask 75 randomly chosen students at a school how many movies they watch each week. If there are 1200 students in the school, estimate the number of students who watch one movie per week.

900

210

840

336

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Identify the population and sample for each example.

Population: Students

Sample: Members of the football team

Population: Members of the football team

Sample: Students

Population: Students

Sample: Students that have had a broken bone

Population: Members of the football team

Sample: Members of the football team that have broken a bone.

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

8.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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) ?

9.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.

10.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.

Estimating Differences Between Populations Using Samples

20 questions

_______ is a part of a group being surveyed.

237 fifth graders and 346 fourth graders went on a field trip. Estimate how many more fourth graders were on a field trip than fifth graders.

You ask 75 randomly chosen students at a school how many movies they watch each week. If there are 1200 students in the school, estimate the number of students who watch one movie per week.

Identify the population and sample for each example.

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