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 boxplc indicates there are no outliers. Complete parts (a) through (c) below. \[ \begin{array}{llllllll} 68.43 & 79.44 & 68.97 & 84.95 & 79.09 & 85.46 & 101.97 & 99.13 \end{array} \] ت 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 $\$ 83.43$. (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 $\square \%$ confident that the all cities have a travel tax between $\$ \square$ and $\$ \square$. B. One can be $\square \%$ confident that the mean travel tax for all cities is between $\$ \square$ and $\$ \square$. C. There is a $\square \%$ probability that the mean travel tax for all cities is between $\$ \square$ and $\$ \square$. D. The travel tax is between $\$ \square$ and $\$ \square$ for $\square \%$ of all cities.
Solution
Step 1 ：Given the data of total travel tax for a 3-day business trip in 8 randomly selected cities, we are asked to determine a point estimate for the population mean travel tax and construct a 95% confidence interval for the mean tax paid for a three-day business trip.
Step 2 ：The point estimate for the population mean travel tax can be calculated by finding the average of the given data. The data is [68.43, 79.44, 68.97, 84.95, 79.09, 85.46, 101.97, 99.13]. The average of these values is \$83.43.
Step 3 ：The 95% confidence interval can be calculated using the formula for a confidence interval which is `mean ± (t*std_dev/sqrt(n))` where `t` is the t-score for a 95% confidence interval, `std_dev` is the standard deviation of the sample, and `n` is the number of observations in the sample.
Step 4 ：The t-score for a 95% confidence interval with 7 degrees of freedom (n-1) is approximately 2.365. The standard deviation of the sample is approximately 12.34. The number of observations in the sample is 8.
Step 5 ：Substituting these values into the formula, we get the 95% confidence interval as (73.12, 93.74).
Step 6 ：Final Answer: The point estimate for the population mean travel tax is \( \boxed{83.43} \). One can be 95% confident that the mean travel tax for all cities is between \( \boxed{73.12} \) and \( \boxed{93.74} \).
