Answer the following questions:

Q11:

The test statistic is 11.54'. (Round to two decimal places as needed.) The critical value is 12.833'. (Round to three decimal places as needed.) Conductthe hypothesis test and provide the test statistic and the critical value, and state the conclusion. A company claims that its packages of 100 candies are distributed with the following color percentages: 14% red, 13% orange, 16% yellow, 11% brown, 24% blue, and 17% green. Use the given sample data to test the claim that the color distribution is as claimed. Use a 0.025 signicance level. g Click the icon to View the colorcounts for the candy in the package. Click here to View the chi-square distribution table. An investigator analyzed the leading digits from 776 checks issued by seven suspect companies. The frequencies were found to be 2, 16, 5, 53, 206, 464, 5, 18, and 7, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.05 signicance level to test for goodness-oft with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit 1 2 3 4 5 6 7 8 9 Actual Frequency 2 16 5 53 206 464 5 18 7 Benford's Law: Distribution of Leading Digits 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% Determine the null and alternative hypotheses. % Calculate the test statistic, x2. x2 = 3,551.306' (Round to three decimal places as needed.) Calculate the P-value. P-value = 0.0000' {Round to four decimal places as needed.) Polygraph test indicated that the subject lied. Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) 7 36 Polygraph test indicated that the subject did not lie. 12 15 Determine the test statistic. 12 = 17.460' (Round to three decimal places as needed.) Determine the P-value of the test statistic. P-value = 0.0000' (Round to four decimal places as needed.) The table below includes results from polygraph (lie detector) experiments conducted by researchers. In each case, it was known if the subjected lied or did not lie, so the table indicates when the polygraph test was correct. Use a 0.05 signicance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truth and lies? E Click the icon to view the table. Determine the test statistic. 12 = 5.831' (Round to three decimal places as needed.) Determine the P-value of the test statistic. P-value = 0.0157' {Round to four decimal places as needed.) Results from a civil servant exam are shown in the table to the right. Is there sufcient evidence to support the claim that the results from the test are discriminatory? Use a 0.01 signicance level. Passed Failed Q White candidates 20 19 Minority 9 29 ca nd i dates 4/17/2021 Chi-square distribution table Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 0.412 0.554 0.831 1.145 1.610 9.236 11.071 12.833 15.086 16.750 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.278 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.955 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188