QUESTION 1.

The E; expected count for the two categories, i = 1, 2, are E, = 75 and E, = 25. The O, observed counts can be found in the data table below along with the expected counts. Use this information to compute the X test statistic, rounded to two decimal places. Red Petals Streaky Petals Observed Count 52 48 Expected Count 75 25 X2 = (0; - E;)2 E; (01 - E, )2 + (02 - E,)2 = E1 E2 = (52 - 75)2 - 25 + 75 25 The degrees of freedom for a multinomial experiment consisting of k-categories or cells where the test statistic has an approximate x distribution is computed as of = k - 1. Since the data has been classified into two categories, k = , and the degrees of freedom for this test statistic is df = 1.The percentage of various colours are different for the "peanut" variety of Mars M&M candles, as reported on the Mars, Inc. website. What Colours Come In Your Bag? Brown a 12% Yellow 0 15% Bed 0 12% Blue 00 23% 99 W. Green 0 15% A 400-gram bag of peanut M&Ms is randomly selected and contains 71 brown, 88 yellow, 62 red, 116 blue, 106 orange, and 87 green candies. Do the data substantiate the percentages reported by Mars, Inc.? Use the appropriate test and describe the nature of the differences, if there are any. (Use a = 0.05. Round your answers to three decimal places.) 1-2. Null and alternative hypotheses: O Ho: P1 = 6: P2 = 6:P3 = 6:14= =;P5= P6 Ha: At least one p; is different from O Ho: P1 = 0.12; P2 = 0.15; P3 = 0.12; P4 = 0.23; P5 = 0.23; P6 = 0.15 Ha: At least one p; is different from the specified value O Ho: P1 = 0.12; P2 = 0.15; P3 = 0.12; P4 = 0.23; P5 = 0.23; P6 = 0.15 Ha: No value of p; is the same as its specified value O Ho: At least one p; is different from _ Ha : P 1 = = ; P2 = =; P3 = -; P4 = 7:P5 = 6:16=6 O Ho: P1 = 0.12; P2 = 0.15; P3 = 0.12; P4 = 0.23; P5 = 0.23; P6 = 0.15 Ha: At least two p; are different from the specified value 3. Test statistic: X2 = 4. Rejection region: X2 >0n the fortieth anniversary ofJFK's assassination, a certain poll showed most Americans disagree with the government's conclusions about the killing. The Warren Commission found that Lee Harvey Oswald acts alone when he shot Kennedy, but many Americans are not so sure. Do you think that we know all the facts about the assassination of President John F. Kennedy or do you think there was a coverrup? Here are tl results from a poll of 900 registered voters countrywide We Know All There Was a the Facts CovePUp (Not Sure) Democrats 43 310 32 Republicans 64 246 46 Independents 21 116 22 (a) Do these data provide sufficient evidence to conclude that there is a difference in voters' opinions about a possible coveraup depending on the political affiliation of the voter? Test using tr : 0.05. (Round your answers to three decimal places.) 12. Null and alternative hypotheses: O HO: Voters' opinions about a possible (overtup and voters' political affiliations are dependent. Ha: Voters' opinions about a possible cover-up and voters' political affiliations are independent. 0 H0: Voters' opinions about a possible coversup and voters' political affiliations are linearly related. Ha: Voters' opinions about a possible cover-up and voters' political affiliations are independent. 0 H0: Voters' opinions about a possible covertup and voters' political affiliations are independent. Ha: Voters' opinions about a possible cover-up and voters' political affiliations are linearly related. 0 H0: Voters' opinions about a possible covertup and voters' political affiliations are independent. Ha: Voters' opinions about a possible coverrup and voters' political affiliations are dependent. O H\": The numbers of people who do and do not believe there was a covertup are equal. Ha: The numbers of people who do and do not believe there was a covertup are not equal. 3. Test statistic: X2 : |: 4. Rejection region: X2 > S These data are observations collected using a completely randomized design. Sample 1 Sample 2 Sample 3 3 UT 2 2 W NO 4 5 3 N N (a) Calculate CM and Total SS. (Round your answer for CM to six decimal places and your Total SS to four decimal places.) CM = 114.2857 X Total SS = 35.7143 (b) Calculate SST and MST. (Round your answers to four decimal places.) SST = 19.3643 MST = 9.6821 (c) Calculate SSE and MSE. (Round your answers to four decimal places.) SSE = 16.35 MSE = 1.4863 X (d) Construct an ANOVA table for the data. (Round your answer for F to two decimal places. Round your answers for SS and MS to four decimal places.) Source df SS MS F Treatments 2 19.3643 9.6821 6.5142 Error 11 16.35 1.4863 X Total 13 35.7143