Question

The lower limit of a confidence interval at the 95% level of confidence for the population proportion if a sample of size 200 had 40 successes is: a. 0.2465 b. 0.3390 c. 0.2554 d. 0.1446 e. 0.1535

Answer 1

Solution :

Given that,

n = 200

x = 40

Point estimate = sample proportion = = x / n = 40 / 200 = 0.200

1 - = 1 - 0.200 = 0.8

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

Z = Z_0.05 = 1.645

Margin of error = E = Z * (( * (1 - )) / n)

= 1.645 * (((0.200 * 0.8) / 200)

= 0.04652

A 95% confidence interval for population proportion p is ,

- E

0.200 - 0.04652

0.1535

The 95% confidence interval for the population proportion p is : 0.1535

option e) is correct