Executives at The Thinking Channel are assessing whether their viewers' educational backgrounds differ from the general population of American adults (ages 25 and over). Based on data from a U.S. Current Population Survey, the table outlines the educational attainment levels alongside their respective population percentages:| Highest degree earned | Percent of population ||------------------------|-----------------------|| Less than high school | 12% || High school | 25% || College | 55% || Higher than college | 8% |A random sample of 160 viewers provided data via telephone surveys, revealing the distribution of their highest degrees earned. The top row in the table includes observed frequencies, while the bottom row lists expected frequencies if Thinking Channel viewers mirror American adults in general.The formula for chi-square is given:\[ \frac{(O - E)^2}{E} \]where \( O \) = Observed frequency, \( E \) = Expected frequency.#### Part 1:Complete the table by filling in the missing values and round the expected frequencies to two or more decimal places.| | Less than high school | High school | College | Higher than college | Total ||-----------------------------|-----------------------|-------------|---------|---------------------|-------|| **Observed frequency \( O \)** | 16 | 25 | 111 | 8 | 160 || **Expected frequency \( E \)** | 40.00 | \( \square \) | \( \square \) | 12.80 | || \(\frac{(O - E)^2}{E}\) | 14.40 | \( \square \) | \( \square \) | 1.800 | |#### Part 2:Follow these steps to test the hypothesis that the educational distribution among Thinking Channel viewers matches the general American adult population. Use a 0.10 level of significance.a) Determine the type of test statistic:- [ ] (Choose one)b) Compute the test statistic value and round to two decimal places.c) Identify the critical value and round to two decimal places.d) Based on results, can it be concluded that viewers' educational background distribution differs from the general adult population?- [ ] Yes- [ ] NoComplete the steps to finalize your analysis.

Solution: The given table of data isPart 1Part 2 a. State the hypotheses. Null hypothesis: H0: The distribution of highest degrees earned by Thinking channel viewers is the same as the distribution of highest degrees earned by American adults as whole. Alternative hypothesis: Ha: The distribution of highest degrees earned by Thinking channel viewers is different from the distribution of highest degrees earned by American adults as whole. To test the multiple proportions chi-square test for goodness of fit should be used. Thus, the type of test statistic is chi-square.b. Then, the test statistic isc. The degrees of freedom is Then, the critical value isd. Rejection rule: If the test statistic is greater than 6.251, then reject the null hypothesis. Conclusion: Here, the test statistic is 13.969. This is greater than 6.251. By the rejection rule, reject the null hypothesis. Then, we can conclude that the distribution of highest degrees earned by Thinking channel viewers is different from the distribution of highest degrees earned by American adults as whole. Thus, the correct option is “Yes”.

Math

Statistics

Executives at The Thinking Channel have decided to test whether the educational backgrounds of the channel's viewers are different from the educational backgrounds of Amerikan adults (ages 25 and over) as a whole. The executives have the following information on the American adult population as a whole, abtained from a recent U.S. Current Population Survey. Highest degree earned Less than high school High school College Higher than college Percent of population 12% 25% 55% 8% The executives also abtained data (from telephone surveys) on highest degrees earned for a random sample of 160 American adults who are Thinking Channel viewers. These data are summarized by the first row of numbers in the table below. These numbers are the frequnncies for the degren categories that were abserved in the sample of 160. The second row of numbers gives the axpacted frequencies under the assumption that the distribution of highest degrees earned by Thinking Channel viewers is the same as the distribution of highest degrnes earned by American adults as a whole. The bottom raw of numbers gives the following valun for each of the degree categories. (So-fe) (observnd frequency "Expected frequency) Expected frequency Part 1 Fil in the missing values in thn table. Round your responses for the expected frequencies to two or more dedmal places. Round your responses to three or more decimal places. Send data to Excel Less than high school High school College Higher than college Total Observed frequency Jo 16 25 111 160 Expected frequency 40.00 12.80 5.625 1.800 Part 2 Answer the following to summarize the test of the hypothesis that the distribution of highest degrees earned by Thinking Channel viewers is the same as the distribution of highest degrees earned by American adults as a whole. Use the 0.10 Invel of significance for the test. (a) Determine the type of test statistic to use. Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round your answer to two or mare decimal places.) (e) Find the critical valun. (Round your answer to two or more decimal places.) (4) Can we condude that the distribution of highest degrees earned by Thinking Channel viewers is different from the distribution of highest degrenes earned by American adults as a whole? O Yes ONo