Exam 9: Understanding Sampling Distributions: Statistics As Random Variables

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 approximate probability that less than 50% of the people in the sample are married?

The t-distribution is the sampling distribution for which of the following?

Which one of the following statements is false?

The mean of the sampling distribution for a sample proportion depends on the value(s) of

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 is the standard error of $\overline{x}$ ?

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 mean of the sampling distribution of the sample mean $\overline{x}$ ?

Use the following information for questions: Suppose that 80% of all English majors and 85% of all engineering majors at a Minnesota college wear winter boots when there is snow on the ground. Two independent random samples of 40 English majors and 60 engineering majors are to be selected during a day with snow on the ground and the proportions of students with winter boots are to be calculated. -What is the probability that more English majors than engineering majors in the sample wear winter boots?

Use the following information for questions: In each situation, indicate whether the value given in bold print is . -75% of all students at a school are in favor of more bicycle parking spaces on campus.

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 probability that the 16 students in the sample do not improve, on average? a

Use the following information for questions: Items produced by a certain process are supposed to weigh 90 grams. However, the process is such that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights is normal with a mean of 89.8 grams and a standard deviation of 1.1 gram. -If we have a random sample of 10 of these items, what is the probability that their average weight exceeds 91 grams?

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 50 course grades are to be randomly selected and the average score in the sample calculated. What is the expected value of the average percentage score in the sample of 50 course grades?