Question

Suppose that you are testing the hypotheses Upper H 0​: pequals0.22 vs. Upper H Subscript Upper A​: pnot equals0.22. A sample of size 350 results in a sample proportion of 0.28. ​a) Construct a 95​% confidence interval for p. ​b) Based on the confidence​ interval, can you reject Upper H 0 at alphaequals0.05​? 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)

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.28 - 1.96 * sqrt(0.28 * 0.72 / 350) < p < 0.28 + 1.96 * sqrt(0.28 * 0.72 / 350)

0.233 < p < 0.327

95% CI is ( 0.233 , 0.327)

b)

Since 0.22 is not contained in confidence interval, we have sufficient evidence H0 at 0.05 level.

c)

For sample proportion,

Standard error = Sqrt [ P (1 - p) / n) ] from proportion p

Standard deviation =  Sqrt [ (1 - ) / n) ] from sample proportion

d)

Standard deviation is used to compute confidence interaval

Standard deviation = Sqrt [  (1 - ) / n) ]