Question

ANSWERS SHOULD BE HANDWRITTEN AND DIAGRAMS ARE REQUIRED< PLEASE UNDERLINE THE FINAL ANSWER

1. The decision rule (aka, the rejection region) for testing the following pair of hypotheses at the .01 level of significance when a sample size of 45 is taken.

H₀: p = .45

H_a: p ≠ .45

Answer 1

To Test the Hypothesis

To Test :

H₀ : p = 0.45 versus H₁ : p ≠ 0.45

we can see these is two - tailed test .and n=45 which is greater than 30 then ,

Test Statistic :

the above formula is appropriate for large sample defined when the smaller of n*p₀ and n*(1-p₀) is at least 5.

under H₀ z follows standard normal distribution

here significance level α = 0.01

the critical value is z_{critical value}  = 2.326

Decision Rule : If we reject H₀ at 0.01 significance level then

test statistic z <= - z_0.01 or   test statistic z > =  z_0.01

Decision Rule : If we reject H₀ then z <= -2.326 or z >= 2.326 at 0.01 significance level

critical region :