SCCC 312A – ProSeminar in Statistics

Lecture Homework #8

Due Date: 3/17/2004 (Wednesday)

Part I: (An application of the binomial distribution on deciding “grade inflation”) Historically, the proportion of USC students whose GPA exceeds 3.0 is 0.40. A researcher suspects that there has been some grade inflation at USC. She randomly samples 15 USC students, and determines the number of students in this sample with GPA exceeding 3.0.

a) Assuming that the historical value is still correct, what is the probability that there will be at least 11 students in the sample whose GPA exceeds 3.0? [You may use the binomial tables.]

b) Assuming that the historical value is still correct, what will be the mean number of students in the sample whose GPA exceeds 3.0? What will be the standard deviation?

c) Suppose now that in the sample that was actually obtained, 12 of the students have GPA exceeding 3.0. What conclusions could you make? In particular, could the researcher conclude that in the population of USC students, the proportion with GPA exceeding 3.0 is now different from the historical value of .4? Explain your reasoning.

d) Compute the probability in a) but assuming that the proportion of USC students with GPA exceeding 3.0 is 0.8. For this population proportion, is it more likely to observe the sample that has been obtained (ie, 12 students with GPA exceeding 3.0) compared to when the proportion is .4?

Part II: Book problems pertaining to the normal distribution.

On pages 244-245 do: 6.11, 6.16, 6.21af, 6.22ad, 6.23a, 6.29

On pages 255-256 do: 6.44, 6.48, 6.49, 6.53