Statistics Questions

Q1) A researcher plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a pre-study was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots.
a) Conduct a Chi-Square Test for Goodness of Fit. (Use a .05 significance level and make sure you show all 5 steps of the hypothesis test)
b) Use the results of the Chi-Square test to describe the appeal of the food rewards.

Q2) A principal at a small school wanted to know if the racial makeup of the school staff mirrored that of the student body. The student body broke down into the following racial composition: 31 were White, 18 were Latino, 10 were African American, and 6 were other races. Of the staff members, 42 were White, 4 were Latino, 15 were African American, and 4 were other races.
a) Conduct a Chi-Square Test for Goodness of Fit to determine if the racial makeup of the staff members is different from that of the students. This can be done by treating the racial composition of the students as the expected frequency for the observed frequency of the racial composition of the staff. (Use a .05 significance level and make sure you show all 5 steps of the hypothesis test)

Q3) A new school district superintendent was preparing to reallocate resources for physically impaired students. He wanted to know if the schools in his district differed in the distribution of physically impaired students. He tested samples of 20 students from each of his five schools. He found the following:
School 1: 4 impaired and 16 unimpaired students
School 2: 1 impaired and 19 unimpaired students
School 3: 6 impaired and 14 unimpaired students
School 4: 3 impaired and 17 unimpaired students
School 5: 7 impaired and 13 unimpaired students
a) Conduct a Chi-Square Test for Independence to determine if “School Location” and “Physical Impairment” are dependent on each other. (Use a .01 significance level and make sure you show all 5 steps of the hypothesis test)

Q4) An advertising firm wanted to target television advertisements for people who dine out often. The firm conducted a study in which 75 randomly selected people noted what they watched for a week, and then they were categorized according to the type of show they watched most. They also completed a questionnaire about how often they dine out, and were divided into those that do and do not dine out often. The results were:
Dine Out Often Group               Dine Out Rarely Group
Quiz Shows: 3                           Quiz Shows: 8
Sit Coms: 9                               Sit Coms: 6
Movies: 7                                  Movies: 13
News: 8                                     News: 3
Soap Operas: 3                         Soap Operas: 15
a) Conduct a Chi-Square Test for Independence to determine if “TV Program” and “Dining Out” are dependent on each other. (Use a .05 significance level and make sure you show all 5 steps of the hypothesis test)
b) Calculate Cramer’s Phi and report its magnitude.

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