Chapter 9 Lab

1. A student wants to estimate the wait time at Walmart. She obtains a sample of 9 wait times, in seconds, collected during various times of the day. These times are shown below:

Wait time at Walmart

151.09

121.60

141.78

120.06

140.44

126.91

127.35

122.62

126.62

a) Find a point estimate for the average wait time at Walmart.

b) What conditions do you need to check before creating your confidence interval

c) Find a 97% confidence interval for the average wait time at Walmart. Write an interpretation of the results in the context of the problem.

2. The following is a lower bound and upper bound for a confidence interval for a population mean. Lower bound: 50, upper bound: 88.

a) What is the point estimate for the population mean?

b) What is the margin of error for the confidence interval?

3. A school counselor surveys 500 selected students from different schools in her state. She finds that 210 of them come from divorced families.

a) What conditions do you need to check before you construct a confidence interval in this situation? Do they check? Show your work or explain brief

b) Find a 92% confidence interval for the proportion of children who come from divorced families. Interpret the results in the context of the problem. Round to 2 decimal places.

c) The census data from 5 years ago indicated that 39% of students came from divorced families. Based on your confidence interval, do you think the counselor can claim that the percentage of students who come from divorced families has increased? Carefully explain why or why not.

4. The graduate Record Examination (GRE) is a test required for admission to many U. S. graduate schools. Students' scores on the quantitative portion of the GRE follow a normal distribution. (Source: www.ets.org) Suppose a random sample of 10 students took the test, and their scores are given below.

152, 126, 146, 149, 152, 164, 139, 134, 145, 136

a. Find a point estimate of the population mean.

b. Verify the conditions of normality.

c. Construct and interpret a 90% confidence interval for the true mean score for this population

.

d. Interpret the confidence interval that you have created.

5. A group of Brigham Young UniversityIdaho students collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed was 25 mph. The recorded speed (in mph) of 14 randomly selected vehicles is given below.

20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40

a. Assuming speeds are approximately normally distributed, construct a 95% confidence interval for the true mean speed of the drivers in this construction zone. Interpret the interval.

b. Construct a 99% confidence interval for the true mean speed of the drivers in this construction zone. Interpret the interval.

c. Compare the widths of the 95% and 99% confidence intervals.

d. What conclusions can you draw about the speeds people drive in this construction zone?

6. The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Suppose a random sample of 8 students took the test, and their scores are given below.

699, 560, 414, 570, 521, 663, 727, 413

a. Find a point estimate of the population mean.

b. Verify the data could come from a population that is normally distributed.

c. Construct and interpret a 95% confidence interval for the true mean score for the population.

d. How many students should be surveyed to estimate the mean score within 25 points with 90% confidence?

7. A Gallup poll found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

a. What is the sample in this study? What is the population of interest?

b. Based on the results of this survey, obtain a point estimate for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

c. Construct and interpret a 90% confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage. What does this interval suggest?