Exam 9: Understanding Sampling Distributions: Statistics As Random Variables

Which of the following is an example of paired data?

A random sample of 15 high school students is selected for a small experiment in which they will be tested in two ways: a written test and an oral exam. To avoid order effects, eight students are randomly selected to first take the written test and then the oral exam. The remaining 7 students take the tests in reverse order. Summary statistics for the two tests are provided below. What is the standard error of $\overline{d}$ ?

Use the following information for questions: Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. -What is the expected value of the sample mean speed in a random sample of n = 100 cars?

Use the following information for questions: In a pond with a large population of turtles, the percent of three different types of turtles are presented in the table below. A random sample of 100 turtles is taken from the pond. -What is the standard deviation for the sample proportion of chicken turtles?

Use the following information for questions: Scores on an English spelling test are determined for a sample of 16 5^th graders both before and after they learn some new vocabulary "tricks of the trade". In the population of difference scores it is know that students improve with an average of 3 points, with a standard deviation of 4 points, and that the distribution of the differences is approximately normal. -What is the standard deviation of the sampling distribution of the sample mean difference in spelling scores?

Use the following information for questions: In each situation, indicate whether the value given in bold print is . -A 2009 US study found the average age of formal autism diagnosis was 5.7 years, far above the recommended age of 30 months, and that 27% of children remained undiagnosed at age 8 years.

Use the following information for questions: Scores on an English spelling test are determined for a sample of n = 25 fifth graders both before and after they learn some new vocabulary "tricks of the trade". In the population of all differences in scores it is known that students improve with an average of 3 points, with a standard deviation of 4 points, and that the distribution of the differences is approximately normal. -What is the z-score if the mean difference in the sample was $\overline{d}$ = 4.5?

Use the following information for questions: A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at their station. They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so. Suppose that in fact 12% of city residents could name the anchor if asked. -What is the mean of the sampling distribution for the sample proportion of city residents who can name the news anchor on the evening news at their station?

Use the following information for questions: People who go on a (leisure) vacation tend to gain weight. It is thought that the average difference between weight before the vacation and after the vacation is roughly 2 pounds with a standard deviation of 2.5 pounds. Ten vacationing people are to be randomly selected and their weights measured, both upon departure and return of their vacation. -What is the expected value of the sample mean difference between after and before vacation weight?

Use the following information for questions: In each situation, indicate whether it would make more sense to find a confidence interval for the population parameter or to conduct a hypothesis test for a specific null value. -A weight-loss clinic wishes to determine if a certain popular diet actually results in weight-loss.

Use the following information for questions: In a random sample of 250 full time students, 80% preferred to have three one-hour lectures per week rather than two 90-minute lectures. In a random sample of 500 part-time students, 50% said they preferred the three one-hour lectures schedule. The difference between the two sample proportions (full-time - part-time) is to be calculated. -Which of the following choices correctly denotes the difference between the two sample proportions that is to be calculated?

Use the following information for questions: Let p denote the proportion of adults in major minority groups in the US who read an ethnic newspaper at least several times per week. According to the nonprofit organization New California Media the true value of p is 45 percent. We decide to take SRS of 200 adults in major minority groups and calculate $\hat{p}$ , the sample proportion of adults who read an ethnic newspaper at least several times per week. -What is the standard deviation of the sampling distribution of $\hat{p}$ ?

Heights for a sample of n = 4 women are measured. For the sample, the mean is 64 inches and the standard deviation is 3 inches. What is the standard error of the mean?

Use the following information for questions: High school students can be categorized into two groups by the amount of activities they are involved in. Let group 1 consist of all high school students who are very involved in sports and other activities and group 2 consist of all high school students who aren't. The distributions of GPAs in both groups are approximately normal. The mean and standard deviation for group 1 are 2.9 and 0.4, respectively. The mean and standard deviation for group 2 are 2.7 and 0.5, respectively. Independent random samples of 50 high school students are to be selected from both groups (for a total of 100 students). -What is the probability that the average GPAs in the two samples differ by no more than 0.1?

Consider a random sample with sample mean $\overline{x}$ . If the sample size is increased from n = 40 to n = 360, then the standard deviation of $\overline{x}$ will

Use the following information for questions: People who go on a (leisure) vacation tend to gain weight. It is thought that the average difference between weight before the vacation and after the vacation is roughly 2 pounds with a standard deviation of 2.5 pounds. Ten vacationing people are to be randomly selected and their weights measured, both upon departure and return of their vacation. -If we can assume that the differences are normally distributed, what is probability that the ten vacationing people gain an average between 1 and 2 pounds?

Use the following information for questions: Let p denote the proportion of adults in major minority groups in the US who read an ethnic newspaper at least several times per week. According to the nonprofit organization New California Media the true value of p is 45 percent. We decide to take SRS of 200 adults in major minority groups and calculate $\hat{p}$ , the sample proportion of adults who read an ethnic newspaper at least several times per week. -What is the approximate probability that more than half the adults in the sample read an ethnic newspaper at least several times per week?

Use the following information for questions: High school students can be categorized into two groups by the amount of activities they are involved in. Let group 1 consist of all high school students who are very involved in sports and other activities and group 2 consist of all high school students who aren't. The distributions of GPAs in both groups are approximately normal. The mean and standard deviation for group 1 are 2.9 and 0.4, respectively. The mean and standard deviation for group 2 are 2.7 and 0.5, respectively. Independent random samples of 50 high school students are to be selected from both groups (for a total of 100 students). -If the sample mean GPA is to be calculated for both groups and we calculate the difference as involved in activities - not so involved in activities, what is the standard deviation of the sampling distribution of the difference in sample means?

Heights for women are bell-shaped with a mean of 65 inches and standard deviation of 2.5 inches. If a random sample of 25 women is taken, what is the mean of the sampling distribution of $\overline{x}$ ?

Use the following information for questions: A group of 50 students had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie is to be compared with the mean pressure after the movie. In general, blood pressure increases by 5 points after watching something violent happening with a standard deviation of 7 points. -What is the mean of the sampling distribution of the sample mean difference in blood pressure before and after watching a movie containing violence?