Question

Suppose that you are testing the hypotheses

Upper H 0H0​:

pequals=0.160.16

vs.

Upper H Subscript Upper AHA​:

pnot equals≠0.160.16.

A sample of size

300300

results in a sample proportion of

0.220.22.

​a) Construct a

9595​%

confidence interval for p.​b) Based on the confidence​ interval, can you reject

Upper H 0H0

at

alphaαequals=0.050.05​?

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?

​a) The

9595​%

confidence interval for p is

​(nothing​,nothing​).

​(Round to three decimal places as​ needed.)

Answer 1

a)

Sample proportion = 0.22

95% confidence interval for p is

- Z/2 * Sqrt( ( 1 - ) / n) < p < + Z/2 * Sqrt( ( 1 - ) / n)

0.22 - 1.96 * sqrt( 0.22 * 0.78 / 300) < p < 0.22 + 1.96 * sqrt( 0.22 * 0.78 / 300)

0.173 < p < 0.267

95% confidence interval for p is ( 0.173 , 0.267)

b)

Since claimed proportion 0.16 is outside the confidence interval, we have sufficient evidence

to reject H0.

Reject H0 at 0.05 significance level.

c)

For sample proportion standard error = standard deviation

d)

Standard error = standard deviation = Sqrt( ( 1 - ) / n)

= sqrt( 0.22 * 0.78 / 300)

= 0.024