Math homework help

100. What is meant by the term “90% confident” when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would

contain the sample mean.

c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would

contain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the

samples.

106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours.

a.

i. x ¯ = __________

ii. sx = __________

iii. n = __________

iv. n – 1 = __________

b. Define the random variables X and X ¯ in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean time wasted.

i. State the confidence interval.

iii. Calculate the error bound.

e. Explain in a complete sentence what the confidence interval means.

110. Forbes magazine published data on the best small firms in 2012. These were firms that had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion.

The Table 8.13 shows the ages of the corporate CEOs for a random sample of these firms.

48 58 51 61 56

59 74 63 53 50

59 60 60 57 46

55 63 57 47 55

57 43 61 62 49

67 67 55 55 49

114. A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢; 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; $1.50; 40¢; 65¢; 40¢. Assume the underlying distribution is approximately normal.

a.

i. x ¯ = __________

ii. sx = __________

iii. n = __________

iv. n-1 = __________

b. Define the random variables X and X ¯ in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95% confidence interval for the population mean worth of coupons.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. If many random samples were taken of size 14, what percent of the confidence intervals constructed should contain the population mean worth of coupons? Explain why.

124. Another question in the poll was “[How much are] you worried about the quality of education in our schools?” Sixty-three percent responded “a lot”. We are interested in the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

a. Define the random variables X and P′ in words.

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 95% confidence interval for the population proportion of adult Americans who are worried a lot about

the quality of education in our schools.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) is ±3%. In one to three

complete sentences, explain what the ±3% represents.

130. On May 23, 2013, Gallup reported that of the 1,005 people surveyed, 76% of U.S. workers believe that they will continue working past retirement age. The confidence level for this study was reported at 95% with a ±3% margin of error.

a. Determine the estimated proportion from the sample.

b. Determine the sample size.

c. Identify CL and α.

d. Calculate the error bound based on the information provided.

e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between the

values.

f. Create a confidence interval for the results of this study.

g. A reporter is covering the release of this study for a local news station. How should she explain the confidence

interval to her audience?