Exam 9: Understanding Sampling Distributions: Statistics As Random Variables

Which one of the following statements is false?

Use the following information for questions: Every student taking elementary statistics at a large university (1,100 students) participated in a class project by rolling a 6-sided die 100 times. Each individual student determined the proportion of his or her 100 rolls for which the result was a "1". The instructor plans to draw a histogram of the 1,100 sample proportions. -What will be the approximate mean for the 1,100 sample proportions?

Use the following information for questions: Suppose that the weight of apples eaten by individual Americans each year can be described by a normal distribution with mean $\mu$ = 15 pounds and standard deviation $\sigma$ = 5 pounds per year. -For a random sample of n = 16 people, what is the z-score for a sample mean $\overline{x}$ = 10 pounds?

Use the following information for questions: Management of an airline uses a normal distribution to model the value claimed for a lost piece of luggage on domestic flights. The mean of the distribution is $600 and the standard deviation is $85. Suppose a random sample of 65 pieces of luggage is to be selected. -What is the expected value of the average claimed value of the 65 pieces of lost luggage?

Use the following information for questions: In the Youth Risk Behavior Survey (a study of public high school students), a random sample showed that 45 of 675 girls and 103 of 621 boys had been in a physical fight on school property one or more times during the past 12 months. -What is the standard error of the difference in sample proportions?

Which of the following statements is true about the standard deviation of $\overline{x}$ ?

Sleep apnea is a condition involving irregular breathing during sleep. Suppose that 20% of a population of men experience sleep apnea. A random sample of n = 64 men is to be drawn from this population. What is the mean of the sampling distribution for the sample proportion of men who experience sleep apnea?

For which of the following situations would the Rule for Sample Means not apply?

Which of the following statements best describes the relationship between a parameter and a statistic?

Use the following information for questions: In the Youth Risk Behavior Survey (a study of public high school students), a random sample showed that 45 of 675 girls and 103 of 621 boys had been in a physical fight on school property one or more times during the past 12 months. -What is the difference in sample proportions of students who had been in a fight (boys - girls)?

Use the following information for questions: For each study, decide if the two samples are : -A group of 100 students were randomly assigned to receive vitamin C (50 students) or a placebo (50 students). The groups were followed for 2 weeks and the proportions of students with colds were compared.

Use the following information for questions: Suppose height of college students can be modeled by the normal distribution. We believe the mean of the normal distribution is 1.72 m. We randomly sample 18 students and find an average of 1.69 m and a standard deviation of 5 cm (= 0.05 m). -What are the degrees of freedom for the t-distribution?

Use the following information for questions: Contradicting some previous research, a new study finds that frequent use of painkillers does not substantially increase a healthy man's risk of developing hypertension. -The study finds that the observed difference between the two groups was not statistically significant. Explain in your own words what that means.

Use the following information for questions: Many undergraduate students are thinking about getting a graduate degree. Do male and female students have equal opinions about this? A survey of undergraduate students at public universities in the state of California revealed the following results: Out of 265 female students, 131 were seriously thinking about applying to graduate school. Out of 233 male students, 130 were seriously thinking about applying to graduate school. We wish to compare the proportions of male and female students who are thinking about getting a graduate degree by calculating a confidence interval for the difference between males and females. -What is the correct notation for the difference $\frac{130}{233} - \frac{131}{265}$ ?

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. If your answer is "a hypothesis test," specify the null value that you would test. -Dyslexia is a broad term defining a learning disability that impairs a person's ability to read, speak, and spell. It is believed that dyslexia can affect between 5 to 10 percent of the population although there have been no studies to indicate an accurate percentage.

Use the following information for questions: Based on the 2000 Census, 31.8% of grandparents in California are the primary caregivers for their grandchildren. Suppose n = 1000 grandparents are to be sampled from this population and the sample proportion of grandparents as primary caregivers ( $\hat{p}$ ) is to be calculated. -What is the standard deviation of the sampling distribution of $\hat{p}$ ?

Use the following information for questions: For each study, decide if the two samples are : -A group of 50 students each measured the length of their right arm and the length of their left arm. The average right arm lengths were compared to the average left arm lengths.

Use the following information for questions: The level of nitrogen oxides (NOX) in the exhaust of a particular car model can be modeled by the normal distribution with mean 0.9 grams per mile and standard deviation of 0.16 grams per mile. A random sample of 4 of these NOX levels is to be selected. -What is the probability that the NOX level of the first car in the sample is greater than 1 gram per mile?

Use the following information for questions: A group of 50 students each measured the length of their right arm and the length of their left arm. The right arm lengths were compared to the left arm lengths. The average difference between right and left arm lengths was 0.3 cm with a standard deviation of 1 cm. -What is the standard error of the sample mean difference?

Use the following information for questions: We wish to conduct a hypothesis test to determine if, on average, the mother in a family spends more time doing house work per week than the father, for families where both parents have a full time job. -What is the correct notation for the parameter of interest?