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 alpha using the given sample statistics. ​Claim: pnot equals0.24​; alphaequals0.01​; Sample​ statistics: ModifyingAbove p with caretequals0.19​, nequals200

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

= 0.19

P₀ = 0.24

1 - P₀ = 1 - 0.24 = 0.76

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.19 - 0.24 / [(0.24 * 0.76) /200 ]

= -1.66

Test statistic = -1.66

P(z < -1.66) = 0.0485

P-value = 2 * 0.0485 = 0.097

= 0.01

P-value >

Fail to reject the null hypothesis .