The accompanying data represent the total travel tax (in dollars) for a 3-day bu

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. 67.71 78.92 70.31 8363 7948 8576 100.75 9965 Click the icon to view the table of critical t-values (a) Determine a point estimate for the population mean travel tax A point estimate for the population mean travel tax is s (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.) OA The lower bound is S and the upper bound is $ OB The lower bound is S and the upper bound is O c. The lower bound is $ and the upper bound is $ 0 D. The lower bound is $ and the upper bound is $ There sa % probability that the mean travel tax for all cities is between these values. The travel taxis between these values for % of all cities. One can be % confident that al cities have a travel tax between these values. . One can be % confident that the mean travel tax for all cities is between these values (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? O A. The researcher could increase the level of confidence O B. The researcher could increase the sample mean. OC. The researcher could decrease the sample standard deviation. O D. The researcher could decrease the level of confidence.

Explanation / Answer

Solution:- Given data 67.71,78.92,70.31,83.63,79.48,85.76,100.75,99.65

a) A point estimate for the population mean travel tax is $ 83.2763
mean = sum of terms/number of terms
= 666.21/8
= 83.28

b) option D. The lower bound is $73.17 and the upper bound is $93.39.one can be 95% confident that the mean travel tax for all cities is between these values.
=> mean = 83.28 , sd = 12.0922 , df = n - 1 = 7 , t = 2.365
=> X +/- t * s/sqrt(n) = 83.28 +/- 2.365*12.0922/sqrt(8)
= (73.1690 , 93.3909)

c) option D. The researcher could decrease the level of confidence

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