Question

QUESTION 5

From a sample of 500 college students it was found that 300 of them had taken a statistics course.

Construct a 95% confidence interval for the proportion of college students who have taken a statistics course. What is the LOWER BOUND on the interval? Round your answer to three decimal places (i.e. 0.123).

4 points   

QUESTION 6

From a sample of 500 college students it was found that 300 of them had taken a statistics course.

Construct a 95% confidence interval for the proportion of college students who have taken a statistics course. What is the UPPER BOUND on the interval? Round your answer to three decimal places (i.e. 0.123).

Answer 1

Solution :

Given that,

n = 500

x = 300

= x / n = 300/ 500 = 0.6

1 - = 1 - 0.6 = 0.4

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.6 * 0.40) / 500)

= 0.043

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.6 - 0.043 < p < 0.6 + 0.043

0.557 < p < 0.643

(0.557, 0.643)

LOWER BOUND = 0.557

UPPER BOUND = 0.643