**t-Distribution Table**This t-distribution table provides critical values for the t-distribution for various degrees of freedom (df) and corresponding probabilities in the right tail. It is essential for hypothesis testing in statistics, particularly in t-tests.**Graphical Representation:**- The top-left corner features a graph illustrating the t-distribution curve.- The shaded area represents the "Area in right tail," indicating the probability of values falling in this region.**Table Details:**- **Degrees of Freedom (df):** Listed vertically on the left, ranging from 1 to 1000.- **t-values for Different Alpha Levels (Area in Right Tail):** Columns correspond to the alpha levels commonly used in statistical tests: - 0.25 - 0.20 - 0.15 - 0.10 - 0.05 - 0.025 - 0.02 - 0.01 - 0.005 - 0.0025 - 0.001 - 0.0005For each degree of freedom, the table provides the critical t-values required to find the cutoff point where a test statistic would be considered improbable if the null hypothesis were true.**Usage:**When conducting a t-test:- Select the appropriate row based on the degrees of freedom in your analysis.- Choose the column corresponding to your desired significance level (e.g., 0.05 for a 5% significance level).- The intersection provides the critical t-value.This table is crucial for determining whether to reject the null hypothesis in t-testing, thereby making informed decisions based on statistical analyses. **3. 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.**- Data: 68.82, 79.26, 68.51, 84.96, 80.53, 87.25, 101.72, 98.77Click 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 $___________. *(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. The travel tax is between $__________ and $__________ for __________% of all cities.- B. There is a __________% probability that the mean travel tax for all cities is between $__________ and $__________.- C. One can be __________% confident that the mean travel tax for all cities is between $__________ and $__________.- D. One can be __________% confident that 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 increase the level of confidence.- B. The researcher could increase the sample mean.- C. The researcher could decrease the sample standard deviation.- D. The researcher could decrease the level of confidence.

Solution: n = 8 Sample size ∑x =669.82x = ∑xn=669.828=83.73 Sample mean s =∑(x-x)2n-1s =12.2353 Sample standard deviation a) A point estimate for the population mean travel tax is Point estimate = x =$ 83.73 A point estimate for the population mean travel tax is $83.73 b) The 95% confidence for the mean tax paid for a three day business trip is x ±tα/2,n-1×snAt α=0.05tα/2,n-1=t0.025,7=2.365 From t table 83.73±2.365×12.2353883.73±2.365×12.23532.828427(83.73±2.365×4.325832)(83.73±10.23)(83.73-10.23, 83.73+10.23)(73.50, 93.96) The 95% confidence for the mean tax paid for a three day business trip is ( $73.50, $93.96) Interpretation of confidence interval: One can be 95% confident that the mean travel tax for all cities is between $73.50 and $93.96 Option C is Correct c) The reasearcher could increase the level of significance. Option A is Correct