Question

Suppose that you are testing the hypotheses

H0 :p= 0.21 vs HA :p ≠ 0.21

A sample size of 150 results in a sample proportion of 0.26  

​a) Construct a 99​% confidence interval for p.

​b) Based on the confidence​ interval, can you reject H0 at a= 0.01? Explain.

​c) What is the difference between the standard error and standard deviation of the sample​ proportion?

​d) Which is used in computing the confidence​ interval?

Answer 1

a)

b)Since confidence interval includes 0.21, so at 99% confidence level or at 1% significance level, we fail to reject H₀.

c) The major difference between the standard error and the standard deviation is that the standard error is based on the sample statistics whereas the standard deviation is based on the population parameters.

standard deviation of sample proportion

standard error of sample proportion

d) In computing the confidence​ interval, standard error is used.