SOMS 120 A random sample of 35 two-year colleges in 2008–2009

Question 1

Select one answer.

10 points

A random sample of 35 two-year colleges in 2008–2009 collected data on the in-state tuition costs and enrollment totals. Based on the sample, the researchers estimated the mean in-state tuition for all two-year colleges to be $2,380. Which form of statistical inference does this conclusion represent?

1. Point estimation
2. Hypothesis testing
3. Interval estimation

Question 2

Select one answer.

10 points

A researcher conducted a survey of graduating college students. 350 college students were randomly selected to answer the survey. One of the survey questions asked, “How much do you owe in student loans?” The average student loan debt reported by respondents was $42,576 with a standard deviation of $2,801.

$42,576 is the point estimate for which of the following?

1. The mean salary of all college students who graduate college.
2. The proportion of all college students who graduate college in debt.
3. The mean loan debt of all college students who graduate college.
4. The standard deviation of loan debt of all college students who graduate college.

Question 3

Select one answer.

10 points

Based on survey results, the mean amount of credit card debt for U.S. adults under 35 is $8,724. This point estimate would be unbiased and most accurate if the survey were based on which of the following?

1. A random sample of 1,500 U.S. adults under 35
2. A random sample of 2,800 U.S. adults under 35
3. A random sample of 3,000 U.S. college students
4. A national television news station poll with 3,500 responses

Question 4

Select all that apply.

10 points

Suppose we take repeated random samples of 50 college students from the same population and determine a 95% confidence interval for the mean GPA from each sample. Which of the following statements is true regarding the confidence intervals? Check all that apply.

1. The intervals are centered around the population mean GPA.
2. The intervals are centered around the sample mean GPA.
3. 95% of the intervals will contain the sample mean in the long run.
4. 95% of the intervals will contain the population mean in the long run.

Question 5

Select one answer.

10 points

A random sample of 30 students taking statistics at a community college found the student’s mean GPA to be 3.25. A 95% confidence interval for the mean GPA of all students taking statistics at this college was determined to be (3.07, 3.43). What is the margin of error for this confidence interval?

1. 0.36
2. 0.18
3. 3.25
4. 0.95

Question 6

Select one answer.

10 points

Assuming data come from a random sample, under which of the following conditions should we not calculate a confidence interval for a population mean?

1. Population is normally distributed and sample size is 20 individuals.
2. Population distribution is unknown and sample size is 20 individuals.
3. Population distribution is unknown and sample size is 50 individuals.
4. Population is normally distributed and sample size is 50 individuals.

Question 7

Select one answer.

10 points

For the following scenario, is the variable is categorical or quantitative?

A poll of students at your college is asked whether or not they plan to attend graduate school after graduation.

1. Categorical
2. Quantitative

Question 8

Select one answer.

10 points

When the sampling distribution of a statistic centers exactly around the parameter it estimates we can say that the statistic is which of the following?

1. Unbiased
2. Statistically significant
3. Normally distributed
4. Equal to the parameter

Question 9

Select one answer.

10 points

A study was conducted to estimate ?, the mean commute distance that all employed U.S. adults travel to work. Suppose a random sample of 49 employed U.S. adults gives a mean commute distance of 22 miles and that from prior studies, the population standard deviation is assumed to be ? = 8.4 miles.

Based on this information, what would be the point estimate for ??

1. 8.4
2. 49
3. 22
4. 1.2

Question 10

Select one answer.

10 points

A study was conducted to estimate ?, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3.6 hours.

We are 95% confident that the mean number of weekly hours that U.S. adults use computers at home falls between which of the following intervals?

1. 7.3 and 9.7
2. 8.4 and 8.6
3. 6.5 and 10.5
4. 7.7 and 9.3
5. 8.1 and 8.9

Question 11

Select all that apply.

10 points

A study was conducted to estimate ?, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3.6 hours. The 95% confidence interval for the mean, ?, is (7.7, 9.3).

Which of the following will provide a more informative (i.e., narrower) confidence interval than the 95% confidence interval? Check all that apply.

1. Using a sample of size 400 (instead of 81)
2. Using a sample of size 36 (instead of 81)
3. Using a different sample of size 81
4. Using a 90% level of confidence (instead of 95%)
5. Using a 99% level of confidence (instead of 95%)

Question 12

Select one answer.

10 points

A study was conducted to estimate ?, the mean commute distance that all employed U.S. adults travel to work. Suppose a random sample of 49 employed U.S. adults gives a mean commute distance of 22 miles and that from prior studies, the population standard deviation is assumed to be ? = 8.4 miles.

How large a sample of U.S. adults is needed in order to estimate ? with a 95% confidence interval oflength 2.4 miles?

1. 49
2. 111
3. 196
4. 784

Question 13

Select one answer.

10 points

A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples.

If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U.S. adults), what sample size should be used?

1. 17,778
2. 4,445
3. 1,112
4. 67
5. 45