Exam 9: Understanding Sampling Distributions: Statistics As Random Variables

Use the following information for questions: For each study, decide if the two samples are : -In a random sample of 100 students, the change in hours of sleep for each student during and after finals week were compared.

Use the following information for questions: A gasoline tank for a certain car is designed to hold 15 gallons of gas. The manufacturer of this gasoline tank claims that the actual capacity of a randomly selected tank has a distribution that is approximately normal with a mean of 15.0 gallons. A random sample of 25 tanks results in an average of 14.8 gallons with a standard deviation of 0.42 gallons. -What is the standard error of the sample mean?

Use the following information for questions: Suppose that 60% of all teenagers - both boys and girls - are classified as having good grades. Independent random samples of 537 boys and 689 girls who go to school in the Washington, DC, area are to be selected and surveyed and the proportions of teenagers with good grades are to be calculated. -What is the standard deviation of the sampling distribution of the difference between the two sample proportions (boys - girls)?

Use the following information for questions: Many adults complain they do not get enough sleep at night. What happens when these adults have children? Independent random samples of 150 adults who do not have children in the house and 130 adults who do have children in the house are selected. The average amount of sleep the adults without children had was 7.1 hours with a standard deviation of 0.7 hours. The average amount of sleep the adults with children had was 6.5 hours with a standard deviation of 0.8 hours. -What is the estimate for the standard deviation of the sampling distribution of the difference in sample means?

Use the following information for questions: In each situation, indicate whether the value given in bold print is . -Based on the 2000 Census, 39.5% of the California population of residents who are over 5 years old speak languages other than English at home.

A random sample of 20 mixed gender twins is selected and their resting pulse rate is taken after a 5 minute period of relaxing on a sofa. The average resting pulse rate for the male twins was 67 betas per minute and for the female twins it was 73 beats per minute, resulting in $\overline{d}$ = -6 . The standard deviation of the differences in pulse rates between the male and female twins was 3.4 beats per minute. What is the standard error of $\overline{d}$ ?

Use the following information for questions: In each situation, indicate whether the value given in bold print is . -A customs inspector sampled 5 boxes among 20 boxes being shipped from out of the country. He found that one of the five boxes (20%) contained an illegal food item.

Use the following information for questions: A gasoline tank for a certain car is designed to hold 15 gallons of gas. The manufacturer of this gasoline tank claims that the actual capacity of a randomly selected tank has a distribution that is approximately normal with a mean of 15.0 gallons. A random sample of 25 tanks results in an average of 14.8 gallons with a standard deviation of 0.42 gallons. -What is the value of the t-statistic when comparing the sample mean to the average claimed by the manufacturer?

Use the following information for questions: The distribution of quiz, exam, and course grades is known to be left-skewed. The course grades (measured as percentage scores) in upper level statistics classes have a mean of 68 with a standard deviation of 15. -Suppose one course grade is to be randomly selected. Can we calculate the probability that this grade is higher than 75? If yes, calculate it. If no, explain why not.

Use the following information for questions: Exam scores for a large introductory statistics class follow an approximate normal distribution with an average score of 56 and a standard deviation of 5. The average exam score in your lab was 59.5. The 20 students in your lab sections will be considered a random sample of all students who take this class. -What is the probability that the average score of a random sample of 20 students exceeds 59.5?

Suppose you decide to use the 40 students in your Introduction to Philosophy course as a (convenience) sample. You wish to find out more about students' attitudes toward female priests. You decide to compare the proportion of girls who support the idea of a female priest with the proportion of boys. Define the parameter of interest and give the correct notation.

Use the following information for questions: For each study, decide if the two samples are : -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 was compared with the mean pressure after the movie.

Use the following information for questions: Many adults complain they do not get enough sleep at night. What happens when these adults have children? Independent random samples of 150 adults who do not have children in the house and 130 adults who do have children in the house are selected. The average amount of sleep the adults without children had was 7.1 hours with a standard deviation of 0.7 hours. The average amount of sleep the adults with children had was 6.5 hours with a standard deviation of 0.8 hours. -What is the estimate for the difference in mean hours slept at night between adults with and adults without children?

For n = 203 students, the output below gives a summary of responses to "How long did you sleep last night?" Based on the output, what value estimates roughly, for samples of this size, the average difference between the sample mean and the population mean?

Use the following information for questions: A large car insurance company is conducting a study on behavior behind the wheel to explain the fact that male drivers (who tend to be thought of as more aggressive drivers) have more accidents, on average, per year, than female drivers. The average number of accidents per year for male drivers is 2.3 with a standard deviation of 0.8 and for female drivers the mean is 1.7 with a standard deviation of 0.6. Independent random samples of 25 male and 20 female drivers are to be selected to take part in the behavior study. -If the sample mean number of accidents is to be calculated for both the male and female drivers and we calculate the difference as male - female, what is the expected value for the difference in sample means?

Explain what the "sampling distribution of a statistic" means (or give an example).

Use the following information for questions: Suppose that 60% of all teenagers - both boys and girls - are classified as having good grades. Independent random samples of 537 boys and 689 girls who go to school in the Washington, DC, area are to be selected and surveyed and the proportions of teenagers with good grades are to be calculated. -What is the probability that the difference between the two sample proportions (boys - girls) is greater than 5 percentage points (0.05)?

If the size of a sample randomly selected sample from a population is increased from n = 100 to n = 400, then the standard deviation of $\hat{p}$ will

Use the following information for questions: Suppose that 60% of all teenagers - both boys and girls - are classified as having good grades. Independent random samples of 537 boys and 689 girls who go to school in the Washington, DC, area are to be selected and surveyed and the proportions of teenagers with good grades are to be calculated. -What is the mean of the sampling distribution of the difference between the two sample proportions (boys - girls)?

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 probability that the sample mean speed in a random sample of n = 100 cars exceeds 68 mph?