Question

Suppose that you are testing the hypotheses H0?: p=0.17 vs. HA?: p?0.17. A sample of size 200 results in a sample proportion of 0.22.

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

?b) Based on the confidence? interval, can you reject H0 at ?=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

Ans:

Given that

Sample proportion=0.22

n=200

a)99% confidence interval for p

=0.22+/-2.576*sqrt(0.22*(1-0.22)/200)

=0.22+/-0.075

=(0.145, 0.295)

b)As,99% confidence interval for p includes 0.17 within its limits,so we do not reject H₀.

c)

Standard error uses the sample proportion and standard deviation uses population proportion.

standard deviation for sample proportion:

standard error for sample proportion:

d)Standard error is used for computing the confidence interval.