Unit 7 Progress Check: MCQ Part A

A sociologist is studying the social media habits of high school students in a school district. The sociologist wants to estimate the average total number of minutes spent on social media per day in the population. A random sample of 50 high school students was selected, and they were asked, “How many minutes per day, on average, do you spend visiting social media sites?"

Which of the following is the most appropriate inference procedure for the sociologist to use?

• A one-sample z-interval for a population proportion

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

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

• A two-sample z-interval for a difference between proportions

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

To study the effectiveness of a certain adult reading program, researchers will select a random sample of adults who are eligible for the program. The selected adults will be given a pretest before beginning the program and a posttest after completing the program. The difference in the number of correct answers on the pretest and the number of correct answers on the posttest will be recorded for each adult in the sample.

Which of the following is the most appropriate inference procedure for the researchers to use to analyze the results?

• A one-sample z-interval for a population proportion

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

• A matched-pairs t-interval for a population mean difference
  

• A matched-pairs t-interval for a sample mean difference

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

A researcher studying the sleep habits of teens will select a random sample of n teens from the population to survey. The researcher will construct a t-interval to estimate the mean number of hours of sleep that teens in the population get each night. Which of the following is true about the t-distribution as the value of n decreases from 40 to 20 ?

• The center decreases, and the area in the tails of the distribution increases.

• The center increases, and the area in the tails of the distribution decreases.

• The center remains constant, and the area in the tails of the distribution remains constant.

• The center remains constant, and the area in the tails of the distribution decreases.

• The center remains constant, and the area in the tails of the distribution increases.

What happens to a t-distribution as the degrees of freedom increase?

• The center increases, and the area in the tails increases.

• The center increases, and the area in the tails decreases.

• The center increases, and the area in the tails remains constant.

• The center remains constant, and the area in the tails increases.

• The center remains constant, and the area in the tails decreases.

A recent study of 1,215 randomly selected middle school students revealed that the average number of minutes they spent completing homework during the school week was 180 minutes with a standard deviation of 45 minutes. Which of the following is the standard error, in minutes, of the sampling distribution of the mean number of minutes spent on homework per week for all middle school students?

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The mean and standard deviation of a random sample of 7 baby orca whales were calculated as 430 pounds and 26.9 pounds, respectively. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the mean weight of all baby orca whales?

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To estimate the average cost of flowers for summer weddings in a certain region, a journalist selected a random sample of 15 summer weddings that were held in the state. A graph of the sample data showed an approximately symmetric distribution with no outliers. The sample mean and standard deviation were $734 and $102, respectively. The journalist will create a 95 percent confidence interval to estimate the population mean. Have all conditions for inference been met?

• Yes, all conditions have been met.

• No, the 15 weddings in the sample were not selected at random.

• No, the sample size is not large enough to assume the sampling distribution of sample means is approximately normal.

• No, because the graphical display is approximately symmetric it cannot be assumed that the sampling distribution of sample means is approximately normal.

• No, the sample size of 15 is not less than 10 percent of all weddings in the state.

At a high school with over 500 students, a counselor wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean.

Which of the following conditions for inference have not been met?

1. I. The data are collected using a random sampling method.

2. II. The sample size is large enough to assume normality of the distribution of sample means.

3. III. The sample size is less than 10 percent of the population size.

• I only

• II only

• III only

• I and II only

• I, II, and III

Researchers studying the sticky droplets found on spider webs will measure the widths of a random sample of droplets. From the sample, the researchers will construct a 95 percent confidence interval to estimate the mean width of all such droplets. Which of the following statements about a 95 percent confidence interval for the mean width is correct?

• The interval will be narrower if the researchers increase the level of confidence to 99 percent.

• The interval will be narrower if the researchers increase the sample size of droplets.

• The interval will be wider if the researchers decrease the level of confidence to 90 percent.

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  The interval will be wider if the researchers increase the sample size of droplets.

• The width of the interval will not be affected if the researchers increase or decrease the number of droplets in the sample.

Researchers collected two different samples, X and Y, of temperatures, in degrees Celsius, of the habitat for Florida scrub lizards. The confidence interval 36±1.66 was constructed from sample X, and the confidence interval 36±1.08 was constructed from sample Y. Assume both samples had the same standard deviation. Which of the following statements could explain why the width of the confidence interval constructed from X is greater than the width of the confidence interval constructed from Y?

• The sample size of X is greater than the sample size of Y, and the confidence level is the same for both intervals.

• The sample size of X is greater than the sample size of Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y.

• The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is less than the confidence level used for the interval constructed from Y.

• The sample size is the same for X and Y, and the confidence level is the same for both intervals.

• The sample size is the same for X and Y, and the confidence level used for the interval constructed from X is greater than the confidence level used for the interval constructed from Y.