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 an experiment, students taking French are randomly divided into two groups. Half of the students first take a written exam and a week later an oral exam. The other half of the students take the exams in reverse order. The grades of the oral exam were then compared to the grades of the written exam.

Use the following information for questions: Assume the cholesterol level in a certain population has mean $\mu$ = 200 and standard deviation $\sigma$ = 24. The cholesterol levels for a random sample of n = 9 individuals are measured and the sample mean $\overline{x}$ is determined. -What is the z-score for a sample mean $\overline{x}$ = 180?

Use the following information for questions: At a small college somewhere on the East coast, 20% of the girls and 30% of the boys smoke at least once a week. Independent random samples of 75 girls and 100 boys are to be selected and the proportions of smokers in the samples are to be calculated. -What is the mean of the sampling distribution of the difference in the sample proportion of girl smokers and the sample proportion of boy smokers?

Use the following information for questions: Grade school students, especially the ones in higher grades, tend to spend a lot of time on the computer already. The average amount of time 4^th grade boys spend on the computer is 5 hours per week, with a standard deviation of 1 hour. For 5^th grade boys the average increases to 7 hours per week with a standard deviation of 1.5 hours. Random sample of 20 4^th grade students and 25 5^th grade students are to be selected. -What is the expected value for the difference in sample means (5^th − 4^th grade)?

Use the following information for questions: Based on the 2000 Census, the proportion of the California population aged 15 years old or older who are married is p = 0.524. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of married persons ( $\hat{p}$ ) is to be calculated. -What is the standard deviation of the sampling distribution of $\hat{p}$ ?

Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population?

A fourth grade class of 28 students is given a standardized math test, both at the beginning of the semester and again at the end of the semester. The mean scores from the beginning and the end are compared. Which statistic is being studied?

Use the following information for questions: In a random sample of 50 men, 40% said they preferred to walk up stairs rather than take the elevator. In a random sample of 40 women, 50% said they preferred the stairs. The difference between the two sample proportions (men - women) is to be calculated. -What is the standard error for the difference between the two sample proportions?

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 $\overline{d}$ = 0?

Use the following information for questions: For each study, decide if the two samples are : -A study compared the average number of courses taken by a random sample of 100 freshmen at a university with the average number of courses taken by a separate random sample of 50 freshmen at a community college.

Use the following information for questions: Based on the 2000 Census, the proportion of the California population aged 15 years old or older who are married is p = 0.524. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of married persons ( $\hat{p}$ ) is to be calculated. -What is the mean of the sampling distribution of $\hat{p}$ ?

Use the following information for questions: At a small college somewhere on the East coast, 20% of the girls and 30% of the boys smoke at least once a week. Independent random samples of 75 girls and 100 boys are to be selected and the proportions of smokers in the samples are to be calculated. -What is the standard deviation of the sampling distribution of the difference in the sample proportion of girl smokers and the sample proportion of boy smokers?

Use the following information for questions: Ms. Jackson of the Employment Agency believes that the agency receives an average of 16 complaints per week. Mr. Vermeer, the boss, thinks it is less. A sample of 10 weeks yields an average of 14 complaints per week with a standard deviation of 3 complaints. -What is the standard error of the sample mean?

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 expected value of the sample mean difference in spelling scores?

Statistic is to sample as parameter is to

In a city with a large population of cats, 1 of every 7 cats is a stray cat. In a random sample of n = 25 cats from this city, 5 are strays. What is the z-score associated with the observed sample proportion of stray cats?

If the sample size (n) is large, and the sample is a random sample, then the distribution of the sample proportion $\hat{p}$ is approximately a

Use the following information for questions: Data collected over several years shows that of all patients that come to the doctor's office with a sore throat, 6% of them have a contagious virus. The next 188 patients with a sore throat are tested for this virus. -What is the mean of the sampling distribution of $\hat{p}$ , the sample proportion of patients with a sore throat who have the virus?

Suppose that a polling organization surveys n = 400 people about whether they think the federal government should give financial aid to the airlines to help them avoid bankruptcy. In the poll, 300 people say that the government should provide aid to the airlines. Which choice gives the correct notation and value for the sample proportion in this survey?

Suppose that the mean of the sampling distribution for the difference in two sample proportions is 0. This tells us that