Question

Decide whether the normal sampling distribution can be used. If it can be​ used, test the claim about the population proportion p at the given level of significance

alphaα

using the given sample statistics.​Claim:

pnot equals≠0.24​;

alphaαequals=0.10​;

Sample​ statistics:

ModifyingAbove p with caretpequals=0.21​,

nequals=200

Can the normal sampling distribution be​ used?

state the null and alternative hypothesis.

determine the critical value.

find the z-test statistic.

what is the result of the test?

Reject

Upper H 0H0.

The data provide sufficient evidence to support the claim.

B.Fail to reject

Upper H 0H0.

The data do not provide sufficient evidence to support the claim.

C.Reject

Upper H 0H0.

The data do not provide sufficient evidence to support the claim.

D.Fail to reject Upper H 0H0.

The data provide sufficient evidence to support the claim.

E.

The test cannot be performed.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.24

H_a : p 0.24

n = 200

= 0.21

P₀ = 0.24

1 - P₀ = 1 - 0.24 = 0.76

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.21 - 0.24 / [(0.24 * 0.76) / 200]

= -0.99

Test statistic = -0.99

= 0.10

/ 2 = 0.10 = 0.05

Z_/2 = Z_0.05 = 1.645

critical value = 1.645

Test statistic > critical value

Reject the null hypothesis .

A) The data provide sufficient evidence to support the claim.