First 2 questions are connected to the scenario below.

We would like to compare the grade distributions for three different science courses at a large university. Random samples are selected from first-year biology, chemistry, and physics courses and their final grades are summarized in the table below, as well as some expected cell counts and some cell chi-square values:

Observed Expected Cell Chi-Square Biology Chemistry Physics Row Total

A+ 17 25 18 60

A 32 22 15 69

B+ 24 18 17 59

B 38 28 26 92

C+ 18 20 19 57

C 31 34 31 96

D 16 17 21 54

F 7 14 18 39

Column Total 183 178 165 526

We would like to conduct a hypothesis test to determine whether the distribution of final grades is homogeneous across the three courses.

1. What is the expected number of physics students who would receive a grade of A if the distribution of final grades is homogeneous across the three courses? Give your answer to 2 decimal places.

2. What is the critical value for the appropriate test of significance at the 1% level of significance?

3. We would like to construct a confidence interval to estimate the proportion of all Indians who have brown eyes. What sample size is required in order to estimate the proportion to within 0.04 with 98% confidence?

Do not use an educated guess for the value of p.