Grade distribution: A statistics teacher claims that, on the average, 20% of her students get a grade of A, 35% get a B, 25% get a C, 10% get a D, and 10% get an F. The grades of a random sample of 100 students were recorded. The following table presents the results. A BC D F 5 4 Grade Observed 29 42 20 a. How many of the students in the sample got an A? How many got an F? b. Compute the expected frequencies. c. Which grades were given more often than expected? Which grades were given less often than expected? d. What is the value of x2? e. How many degrees of freedom are there?

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question. a. A sample of 100 students were recorded. From the sample 29 of the students got grade A and 4 f the students got grade F. Thus, 29 students in the sample got an A and 4 students in the sample got an F. b. The expected frequencies are, Grade Percent Expected Frequencies A 20 100×0.20=20 B 35 100×0.35=35 C 25 100×0.25=25 D 10 100×0.10=10 F 10 100×0.10=10 The expected frequencies are, Grade Expected Frequencies A 20 B 35 C 25 D 10 F 10c. Grade Observed (O) Expected Frequencies (E) A 29 20 B 42 35 C 20 25 D 5 10 F 4 10 It can be observed that, the observed grades A and B are more often than expected frequencies. Also, the observed grades C, D and F are less often than expected frequencies. Thus, grades A and B are given more often than expected, grades C, D and F are less often than expected.d. The chi-square test statistic is, χ2=∑O-E2E=29-20220+42-35235+20-25225+5-10210+4-10210=4.05+1.40+1.00+2.50+3.60=12.55 Thus, χ2=12.55.e. For k different groups, the degrees of freedom for chi-square is, df=k-1=5-1=4 Thus, the degrees of freedom is 4.