Students in an introductory statistics class at a large university were classified by birth order and by the college they attend. Complete Birth Order (1 = oldest or only child) Question list K parts a through f. College Total D Click the icon to view the expected values and standardized residuals. Arts and Sciences 58 Question 10 Agriculture 100 Social Science 42 Professional 24 Total 234 Question 11 Question 12 O A. A chi-square test for independence would be appropriate. O B. A chi-square test for goodness-of-fit would be appropriate. Question 13 O C. A chi-square test for homogeneity would be appropriate. b) State your hypotheses. Question 14 Ho HA: Question 15 c) State and check the conditions. Select all the conditions the problem satisfies A. 10% condition: The 234 students are less than 10% of all statistics students. OB. Counted data condition: The data are given as counts. Question 16 C. Randomization condition: This is not a random sample of students, but there is no reason to think that this group of students is not representative, at least of statistics students at this university. D. Expected cell frequency condition: The expected values are all at least 5. Question 17 E. Independence assumption: The students are independent of each other. d) How many degrees of freedom are there? Question 18 of = 0 e) The calculation yields, x" = 19.93. with P = 0.0183. State your conclusion. (Assume a significance level of 0.05.) Question 19 Choose the correct answer below. A. Reject the null hypothesis. There is evidence of an association between birth order and college among statistics students at this university. O) B. Reject the null hypothesis. There is no evidence of an association between birth order and college among statistics students at this university. Question 20 O C. Fail to reject the null hypothesis. There is evidence of an association between birth order and college among statistics students at this O D. Fail to reject the null hypothesis. There is no evidence of an association between birth order and college among statistics students at this university. university. f) Examine and comment on the standardized residuals. Do they challenge your conclusions? Question 21 O A. Some standardized residuals have a magnitude greater than 1. Any conclusions are invalid. O B. The standardized residuals sum to zero. This means the data is not independent. O C. The standardized residuals do not challenge the conclusions drawn. O D. Some cells with expected counts less than 5 have large residuals, so any conclusion found is suspect