Question

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

	A	B	C	Total
Male	17	10	5	32
Female	3	8	13	24
Total	20	18	18	56

Let ππ represent the percentage of all male students who would receive a grade of C on this test. Use a 95% confidence interval to estimate p to three decimal places.

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

< p <

Answer 1

Given that,

Point estimate = sample proportion = = x / n = 5 / 18 = 0.27 8

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.2778 * 0.7222) / 18)

= 0.207

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.278 - 0.207 < p < 0.278 + 0.207

0.071 < p < 0.485