Question

1.Given below are the number of successes and sample size for a simple random sample from a population. x​= 7, n = 50​, ​98% level. the 98% confidence interval is from _ to _.

Answer 1

The 98% confidence interval for p:

The formula for the CI on parameter p is:



The unbiased point estimator, p is the proportion of “successes” in a Bernoulli trial. As a formula, that’s:

7 p= = 0.14 50

Z_α/2 = 2.326 (from z table)

Therefore, the 98% confidence interval for p:

$0.14-2.326\times \sqrt{\frac{0.14(1-0.14)}{50}}<p<0.14+2.326\times \sqrt{\frac{0.14(1-0.14)}{50}}$

0.14 - 0.049 <p<0.14+0.049

The 98% confidence interval is from 0.091 to 0.189