Researchers are investigating the effectiveness of leg-strength training on cycling performance. A sample of 7 men will be selected to participate in a training program that lasts for one month. Peak power during cycling will be recorded for each man both before training and after training. The mean difference in times will be used to construct a 95 percent confidence interval for the mean difference in the population. When all other things remain the same, which of the following statements about the width of the interval is correct?

The interval will be narrower if 15 men are used in the sample.

The interval will be wider if 15 men are used in the sample.

The interval will be narrower if 5 men are used in the sample.

The interval will be narrower if the level is increased to 99% confidence.

The interval will be wider if the level is decreased to 90% confidence.

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

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.

To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63 ± $17.64. Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?

We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.

We are 95 percent confident that the mean cost of a hospital visit for the parrot owners in the sample is between $44.99 and $80.27.

For all parrot owners in the state, 95 percent of hospital visits for parrot care cost between $44.99 and $80.27.

There is a 0.95 probability that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.

There is a 0.95 probability that the mean cost of a hospital visit for the parrot owners in the sample is between $44.99 and $80.27.

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

No, the sample was not selected at random.

Yes, all conditions have been met.

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

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

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

Most dermatologists recommend that the ideal shower lasts approximately 10 minutes. A researcher suspects that the average shower length of high school students is greater than 10 minutes. To test the belief, the researcher surveyed 125 randomly selected high school students and found that their average shower length was 14.7 minutes. With all conditions for inference met, a hypothesis test was conducted at the significance level of alpha=0.05, and the test produced a p-value of 0.0000. Which of the following is an appropriate conclusion?

The researcher has statistical evidence to conclude that the population mean shower length for high school students is greater than 10 minutes.

The test was flawed because the p-value cannot equal 0

The researcher has statistical evidence to conclude that the sample mean shower length for high school students is greater than 10 minutes.

The researcher does not have statistical evidence to conclude that the sample mean shower length for high school students is greater than 10 minutes.

The researcher does not have statistical evidence to conclude that the population mean shower length for high school students is greater than 10 minutes.

A software company provides specialized resort reservation software that can be tailored to the needs of its customers. The company’s 120 customers pay yearly subscription costs that can vary from customer to customer. The company knows that to be profitable, it needs each customer to be spending at least $23,000 per year, on average. The company selects a random sample of 33 customers and computes a mean of $27,871 and a standard deviation of $309.10. It performs a hypothesis test and computes a very small p-value. The software company concludes that the mean is greater than $23,000. Was it appropriate for the software company to perform the hypothesis test and make the conclusion that was made?

No, because the sample is more than 10 percent of the population, so one of the conditions for conducting a hypothesis test has not been met.

Yes, because the �-value is very small, so the company has sufficient evidence to reject the null hypothesis and conclude that its customers are spending more, on average, than $23,000 per year.

Yes, because the sample size is large enough to perform the hypothesis test.

No, because the sample size is not large enough to perform the hypothesis test.

No, because the distribution of the sample data is skewed.

Which of the following statements correctly explains what happens to the variability of a t-distribution as the sample size increases?

The variability of the t-distribution decreases as the sample size increases because the sample standard deviation approaches the population standard deviation.

The variability of the t-distribution increases as the sample size increases because the sample standard deviation approaches the population standard deviation.

The variability of the t-distribution increases as the sample size increases because the mean of the distribution increases.

The variability of the t-distribution decreases as the sample size increases because the mean of the distribution decreases.

The variability of the t-distribution remains constant as the sample size increases because the t-statistic is defined by the sample standard deviation.

For a t-distribution with sample size 10, P(t≥1.96)≈0.0408 and P(t≤−1.96)≈0.0408 . Which of the following is a property of the t-distribution illustrated by the probabilities?

With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution.

With sample size 10, the tails of the curve of the t-distribution have less area than the tails of the curve of the z-distribution.

With sample size 10, the middle of the curve of the t-distribution has more area than the middle of the curve of the z-distribution.

With sample size 10, the mean of the t-distribution is greater than the mean of the z-distribution.

With sample size 10, the mean of the t-distribution is less than the mean of the z-distribution.

A car company claims that its new car, the GoFast2000, has a gas mileage of 35 miles per gallon (mpg). A consumer group suspects that the true mean gas mileage of the new cars is less than 35 mpg. The group tests 50 randomly selected GoFast2000 cars and finds a sample mean of 34.8 mpg. With all assumptions for inference met, a hypothesis test resulted in a p-value of 0.324. For a significance level of alpha=0.05, which of the following is a correct conclusion?

The p-value is greater than 0.05, and the null hypothesis is not rejected. There is not convincing statistical evidence that the mean is less than 35 mpg.

The p-value is less than 0.05, and the null hypothesis is rejected. There is convincing statistical evidence that the mean is less than 35 mpg.

The p-value is less than 0.05, and the null hypothesis is not rejected. There is not convincing statistical evidence that the mean is less than 35 mpg.

The p-value is greater than 0.05, and the null hypothesis is rejected. There is not convincing statistical evidence that the mean is less than 35 mpg.

The p-value is greater than 0.05, and the null hypothesis is not rejected. There is convincing statistical evidence that the mean is 35 mpg.

A bank manager wants the average time that a customer waits in line to be at most 3 minutes. Customers at the bank have complained about the long wait times. To test whether the average wait time at the bank is greater than 3 minutes, 60 customers were randomly selected as they entered the bank and their wait times were recorded. The mean wait time was 4.7 minutes. A one-sample t-test resulted in a p-value of 0.00031. Which of the following is an appropriate interpretation of the p-value?

If the population mean wait time is 3 minutes, the probability of observing a sample mean wait time of 4.7 minutes or more is 0.00031.

The probability that the population mean wait time is greater than 3 minutes is 0.00031.

The probability that the sample mean wait time is greater than 3 minutes is 0.00031.

If the population mean wait time is greater than 3 minutes, the probability of observing a sample mean wait time of 4.7 minutes or more is 0.00031.

If the population mean wait time is 3 minutes, the probability of observing a sample mean wait time of 4.7 minutes is 0.00031.

For a certain brand of tomato seeds, the seed package claims that it takes 87 days after planting for the tomato plants to produce fruit. Sarah, a botanist, wanted to know whether the mean number of days for the plants to produce fruit where she lives is different from 87 days. She planted 40 seeds and recorded the number of days for each plant to produce fruit. With all conditions for inference met, the hypothesis test was conducted at the significance level alpha=0.05, and the test resulted in a p-value of 0.0752. Which of the following is a correct conclusion?

Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.

Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days.

Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.

Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days.

Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is equal to 87 days.

A six-week fitness program was designed to decrease the time it takes retired individuals to walk one mile. At the beginning of the program, 20 randomly selected retired individuals were invited to participate, and their times to walk a mile were recorded. After the six-week program, their times to walk a mile were again recorded. Most participants saw little to no improvement in their times to walk one mile; however, a few participants saw drastic improvements in their times to walk one mile. The program director would like to perform a hypothesis test to determine if the program reduces the mean time for retired individuals to walk a mile. Which of the following statements is true?

Because the sample size of 20 is less than 30 and the improvements in walk times in the sample data appear to be skewed, the distribution of sample means should not be assumed to be approximately normal.

Because the walk times before and after the program are paired, a hypothesis test is not appropriate.

The sampling distribution of sample means can be assumed to be approximately normal because the distribution of the sample data is not skewed.

Because the program recruited only retired individuals, the distribution of sample means should not be assumed to be approximately normal.

An environmental agency frequently samples the water in a region to ensure that the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12 randomly selected samples of the water, the agency constructed the 99 percent confidence interval (22.5,⁢28.7). Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?

We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb

For all water in the region, 99 percent of the water contains a level of the contaminant between 22.5 ppb and 28.7 ppb.

We are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.

There is a 0.99 probability that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb

There is a 0.99 probability that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb.

STAT 7.1-5 Quiz

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSS.IC.B.4

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

Tags

CCSS.HSS.IC.B.4

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

Tags

CCSS.HSS.IC.B.4

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSS.IC.B.4

8.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

9.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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.

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

STAT 7.1-5

26 questions

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

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