Question

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.

Values: 67.63 78.57 69.12 83.84 79.23 85.39 101.28 99.91

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

A point estimate for the population mean travel tax is ____.(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 ___% confident that the mean travel tax for all cities is between $___ and $___.

B. The travel tax is between $___and ?$___ for ___?% of all cities.

C.There is a ___?% probability that the mean travel tax for all cities is between ?$___and $___.

D. One can be ___?% confident that the all cities have a travel tax between $___ and $___.

?(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 level of confidence.

B. The researcher could decrease the sample standard deviation.

C. The researcher could increase the level of confidence.

D. The researcher could increase the sample mean.

Answer 1

(a) A point estimate fot the population mean travel tax = $83.12

(b) One can be 95% confident that the mean travel tax for all cities is between $74.46 and $91.78

(c) The researcher could decrease the level of confidence to increase the precision of the interval

Standard deviation = 12.5

Z value corresponding to 95% confidence interval = 1.96

Sample size, n = 8

Thus, margin of error = = = 8.66

Thus, the confidence interval = (83.12 - 8.66, 83.12 + 8.66) = (74.46, 91.78)