8) By how many times does the sample size have to be increased to decrease the margin of error by a factor of

71.

The sample size must be increased by a factor of

enter your response here

to decrease the margin of error by a factor of 71.

(Type a whole number.)

What is the general relationship, if any, between the sample size and the margin of error?

A. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M1.

B.Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M1.

C. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M21.

D. There is no relationship between the sample size and the margin of error.

9) Determine the t-value in each of the cases.

(a) Find the t-value such that the area in the right tail is 0.20 with 18 degrees of freedom.

(Round to three decimal places as needed.)

(b) Find the t-value such that the area in the right tail is 0.25 with 18 degrees of freedom.

(Round to three decimal places as needed.)

(c) Find the t-value such that the area left of the t-value is 0.01 with 29 degrees of freedom. [Hint: Use symmetry.]

(Round to three decimal places as needed.)

(d) Find the critical t-value that corresponds to 90% confidence. Assume 21 degrees of freedom.

(Round to three decimal places as needed.)

10) A simple random sample of size n is drawn. The sample mean, x, is found to be 19.1, and the sample standard deviation, s, is found to be 4.4.

(a) Construct a 95% confidence interval about if the sample size, n, is 35.

Lower bound:

Upper bound:

(Use ascending order. Round to two decimal places as needed.)

(b) Construct a 95% confidence interval about if the sample size, n, is 51.

Lower bound:

Upper bound:

(Use ascending order. Round to two decimal places as needed.)

How does increasing the sample size e affect the margin of error, E?

A.The margin of error increases.

B. The margin of error does not change.

C. The margin of error decreases.

(c) Construct a 99% confidence interval about if the sample size, n, is 35.

Lower bound:

Upper bound:

(Use ascending order. Round to two decimal places as needed.)

Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E?

A.The margin of error increases.

B. The margin of error decreases.

C. The margin of error does not change.

(d) If the sample size is 17, what conditions must be satisfied to compute the confidence interval?

A. The sample size must be large and the sample should not have any outliers.

B. The sample must come from a population that is normally distributed and the sample size must be large.

C. The sample data must come from a population that is normally distributed with no outliers.

11) A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1085 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.46 hours with a standard deviation of 0.66 hour. Complete parts (a) through (d) below.

(a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.

A. Since the distribution of time spent eating and drinking each day is normally distributed, the sample must be large so that the distribution of the sample mean will be approximately normal.

B. The distribution of the sample mean will always be approximately normal.

C. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal.

D. The distribution of the sample mean will never be approximately normal.

(b) There are more than 200 million people nationally age 15 or older. Explain why this, along with the fact that the data were obtained using a random sample, satisfies the requirements for constructing a confidence interval.

A. The sample size is greater than 5% of the population.

B. The sample size is less than 5% of the population.

C. The sample size is greater than 10% of the population.

D. The sample size is less than 10% of the population.

(c) Determine and interpret a 99% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day.

Select the correct choice below and fill in the answer boxes, if applicable, in your choice.

(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)

A. The nutritionist is 99% confident that the amount of time spent eating or drinking per day for any individual is between

enter your response here and enter your response here hours.

B. There is a 99% probability that the mean amount of time spent eating or drinking per day is between

enter your response here and enter your response here hours.

C. The nutritionist is 99% confident that the mean amount of time spent eating or drinking per day is between enter your response here and enter your response here hours.

D. The requirements for constructing a confidence interval are not satisfied.

(d) Could the interval be used to estimate the mean amount of time a 9-year-old spends eating and drinking each day? Explain.

A. No; the interval is about people age 15 or older. The mean amount of time spent eating or drinking per day for 9-year-olds may differ.

B. Yes; the interval is about the mean amount of time spent eating or drinking per day for people people age 15 or older and can be used to find the mean amount of time spent eating or drinking per day for 9-year-olds.

C. No; the interval is about individual time spent eating or drinking per day and cannot be used to find the mean time spent eating or drinking per day for specific age.

D. Yes; the interval is about individual time spent eating or drinking per day and can be used to find the mean amount of time a 9-year-old spends eating and drinking each day.

E. A confidence interval could not be constructed in part (c).

12) The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts (a) through (c) below.

68.92

78.79

70.72

84.19

80.49

87.56

101.97

99.81

(a) Determine a point estimate for the population mean travel tax.

A point estimate for the population mean travel tax is $enter your response here.

(Round to two decimal places as needed.)

(b) Construct and interpret a 95% confidence interval for the mean tax paid for a three-day business trip.

Select the correct choice below and fill in the answer boxes to complete your choice.

(Round to two decimal places as needed.)

A. One can be enter your response here% confident that the all cities have a travel tax between $enter your response here

and $enter your response here.

B. One can be enter your response here% confident that the mean travel tax for all cities is between

$enter your response here and $enter your response here.

C. There is a enter your response here% probability that the mean travel tax for all cities is between

$enter your response here and $enter your response here.

D. The travel tax is between $enter your response here and $enter your response here for enter your response here% of all cities.

(c) What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?

A. The researcher could decrease the sample standard deviation.

B.The researcher could decrease the level of confidence.

C.The researcher could increase the sample mean.

D. The researcher could increase the level of confidence.

13) A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence assuming s=19.3 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?

A 99% confidence level requires enter your response here subjects. (Round up to the nearest subject.)

A 95% confidence level requires enter your response here subjects. (Round up to the nearest subject.)

How does the decrease in confidence affect the sample size required?

A.Decreasing the confidence level decreases the sample size needed.

B.Decreasing the confidence level increases the sample size needed.

C. The sample size is the same for all levels of confidence.