Question

Giving a test to a group of students, the grades and gender are summarized below

	A	B	C	Total
Male	3	12	6	21
Female	10	2	5	17
Total	13	14	11	38

Let ππ represent the percentage of all male students who would receive a grade of C on this test. Use a 80% confidence interval to estimate p to three decimal places.

Enter your answer as a tri-linear inequality using decimals (not percents).

< p <

Answer 1

Total number of students = 13+141+138 = 292

P[  percentage of all male students who would receive a grade of C on this test ] = 21/292

We need to construct the 80% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	21
Sample Size N =	292

The sample proportion is computed as follows, based on the sample size N = 292 and the number of favorable cases X = 21    

The critical value for =0.2 is z_c = 1.282. The corresponding confidence interval is computed as shown below:

Therefore, based on the data provided, the 80% confidence interval for the population proportion is 0.053 < p < 0.091 , which indicates that we are 80\%80% confident that the true population proportion p is contained by the interval (0.053, 0.091)(0.053,0.091).