Please answer all,Question 1. This question refers to a sweepstakes promotion in which respondents were asked to select what color car they would like to receive if they had the winning number. For a random sample of respondents the choices were 24 blue (B), 34 green(G), 66 red(R), and 36 white(W). Test at the 0.05 level the claim that the population prefers each colour equally. The expected value of chi-square (the test statistics) isSelect one:a. 22.412b. 0c. 9.488d. 24.600e. 7.815Question 2. To test whether GENDER (male and female) and NUMBER OF ABSENCES are related, we use the following table. Number of absences 0 1-2 3-5 6+ Gender male 18 18 16 8 female 22 12 4 2 Total: 100.Assume that the sample data are randomly selected. If GENDER and NUMBER OF ABSENCES are independent, the expected number of males with 3-5 absences isSelect one:a. 10b. 20c. 12d. 0e. 15Question 3. In multinomial and goodness of fit problems comparing observed (O) and expected (E) values, which of the following is not true?Select one:a. The distribution that typically applies is the chi-square with degree of freedom df = (# of categories - 1).b. If there is a good fit to the hypothesized distribution, we expect the test statistic chi-square = ?[(O - E)^2/E] to be approximately equal to 0.c. If there is not a good fit to the hypothesized distribution, we expect the test statistic chi-square = ?[(O - E)^2/E] to be large.d. ?O_i = ?E_ie. ?(O_i - E_i) = 0Question 4. An observed frequency distribution is as follows.Number of successes 0 1 2 3 Frequency 5 30 42 23Let X= the number of successes in the samples. Use a 0.01 significance level to test the claim that the observed frequencies fit a binomial distribution for which n=3 and p=2/3. To perform the test, the expected value for each category is required to be at least 5. How many categories are satisfied with that condition?Select one:a. 2b. 3c. 0d. 1e. 4Question 5. To test whether GENDER (male and female) and NUMBER OF ABSENCES are related, we use the following table. Number of absences 0 1-2 3-5 6+ Gender male 18 18 16 8 female 22 12 4 2 Total: 100. Assume that the sample data are randomly selected. If GENDER and NUMBER OF ABSENCES are independent, the expected value of chi-square (the test statistics) isSelect one:a. 3.75b. 0c. 8.750d. 11.136Question 6. An observed frequency distribution is as follows.Number of successes 0 1 2 3 Frequency 5 30 42 23 Let X= the number of successes in the samples. Assume that X has a binomial distribution with n=3 and p=2/3, use the binomial probability formula, what is the expected value corresponding to the category X=3?Select one:a. None of the other anwers is correct.b. 22.2222c. 3.7037d. 44.4444e. 29.6296Question 7. To test whether GENDER (male and female) and NUMBER OF ABSENCES are related, we use the following table. Number of absences 0 1-2 3-5 6+ Gender male 18 18 16 8 female 22 12 4 2 Total: 100. Assume that the sample data are randomly selected. At the 0.05 level of significance, test the claim that GENDER and NUMBER OF ABSENCES are independent. What is the conclusion?Select one:a. There is sufficient sample evidence to claim that gender and number of absences are dependent.b. There is sufficient sample evidence to claim that gender and number of absences are equally.c. p_{female} = p_{male}d. There is insufficient sample evidence to claim that gender and number of absences are dependent.

To test whether GENDER (male and female) and NUMBER OF ABSENCES are related, we use the following table. Number of absences 0 12 35 6+ Gender male 18 18 16 8 female 22 12 4 2 Total: 100. Assume that the sample data are randomly selected. At the 0.05 level of significance, test the claim that GENDER and NUMBER OF ABSENCES are independent. What is the conclusion? Select one: 0 a. There is sufficient sample evidence to claim that gender and number of absences are dependent. C) b. There is sufficient sample evidence