Question 5 (25 points) A researcher is conducting a goodness-of-fit hypothesis test for the claim that the 4 categories occur with the following frequencies: Ho: PA = 0.4; PB = 0.3; Pc = 0.1; PD = 0.2 Round all answers to three decimal places, if necessary. Category Observed Expected Squared frequency frequency Residual A 40 25 12 D 23 Total a. What are the expected frequencies for each category (5 points) b. What are the squared residuals for each category? (5 points) c. What is the chi-square test statistic for this data? (5 points) d. What is the chi-square critical value for a significance level of 0.01? (5 points) e. Would the decision for this hypothesis test be reject H, or do not reject H,? Explain why. (5 points)Question 6 (12 points) To test Ho: 0 = 15.7 and H1: 0 > 15.7, a simple random sample of 25 is obtained from a population that is known to be normally distributed. a. If the sample standard deviation is determined to be 16.5, compute the test statistic. (4 points) b. If the researcher decides to test the hypothesis at o = 0.1 level of significance, determine the critical value. (4 points) c. Give an explanation as to whether the researcher will reject or not reject the null hypothesis. (4 points)Question 7 (15 points) Find the missing values for the following ANOVA summary table: (3 points each) S.S. df M.S. F Between 2311.498 7 (c) (9) Within (a) (b) (d) Total 5837.498 93 (a) S.S. within = (b) Df within = (c) M.S. between = (d) M.S. within = (e) F =Question 3 [21 points} Place the following steps for a correlation hypothesis test in the correct order from first step to last step: {3 points each} Find the critical yalue from the table Write null and alternative hypothesis Reject or fail to reject the null hypothesis Compare the absolute value of the test statistic to the critical yalue sense Conclude there is a linear correlation or not sufficient evidence to conclude there is a linear correlation f. Find the yalue of r [correlation coefficient] 3. Select a significance level alpha Paragraph