This is a t-distribution table that displays critical values for various degrees of freedom and right-tail probabilities. The values are organized in a tabular form, where each row corresponds to degrees of freedom and each column corresponds to a specific area in the right tail of a t-distribution. This table is commonly used in statistics for hypothesis testing, particularly t-tests.### Components of the Table:1. **Degrees of Freedom (df):** - Found in the leftmost column. Ranges from 1 to 100. Degrees of freedom typically relate to the sample size and are used to find the correct row for the critical value.2. **Areas in the Right Tail:** - The columns correspond to the right tail probabilities or alpha levels (e.g., 0.25, 0.20, 0.15, etc.). These values are probabilities that correspond to the critical t-values for one-tailed t-tests.3. **Critical t-Values:** - The intersection of a degree of freedom and an alpha level gives you the critical t-value. This value is used in statistical tests to determine the cutoff point at which you reject the null hypothesis.### Graph Explanation:The small graph in the top left corner illustrates a probability distribution curve. The shaded area labeled "Area in Right Tail" indicates the region under the curve corresponding to the alpha level or significance level. This shaded region helps to visualize how much of the distribution falls beyond the critical t-value.### How to Use the Table:- **Step 1:** Determine the degrees of freedom (usually sample size minus one for a one-sample test).- **Step 2:** Identify the significance level (alpha) for your test (e.g., 0.05 for a 5% significance level).- **Step 3:** Locate the row corresponding to the degrees of freedom and the column corresponding to the desired alpha level to find the critical t-value.- **Step 4:** Compare your calculated t-statistic to the critical t-value to decide whether to reject the null hypothesis.This table is an essential tool for statisticians working with smaller sample sizes or when the population standard deviation is unknown. 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.Travel tax values: 68.92, 79.66, 69.56, 64.65, 80.91, 87.03, 101.01, 98.34Click 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. One can be __ % confident that all cities have a travel tax between $ __ and $ __.B. One can be __ % confident that the mean travel tax for all cities is between $ __ and $ __.C. There is a __ % probability that the mean travel tax for all cities is between $ __ and $ __.D. The travel tax is between $ __ and $ __ for % 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 increase the level of confidence.B. The researcher could increase the sample mean.C. The researcher could decrease the level of confidence.D. The researcher could decrease the sample standard deviation.

Name: This is a t-distribution table that displays critical values for vari
Uploaded: 2024-03-20T07:07:12.000Z
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Description: This is a t-distribution table that displays critical values for various degrees of freedom and right-tail probabilities. The values are organized in a tabular form, where each row corresponds to degrees of freedom and each column corresponds to a s