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Chapter 9: Q.40 (page 562)

A test of H0:p=0.65against Ha:p<0.65has test statistic z = -1.78.

(a) What conclusion would you draw at the 5% significance level? At the 1% level?

(b) If the alternative hypothesis were H0:p=0.65, what conclusion would you draw at the 5% significance level? At the 1% level?

Short Answer

Expert verified

a. At 5%the null hypothesis gets rejected and at 1%it is not rejected.

b. At the 5%significance level and at the 1%level the null hypothesis doesn't get rejected.

Step by step solution

01

Introduction

The null hypothesis recommends that no measurable relationship and importance exists in a bunch of given single noticed variables, between two arrangements of noticed information and estimated peculiarities.

02

Explanation Part (a)

The null and alternative hypotheses are,

H0:p=0.65Ha:p<0.65

Test statistic z = -1.78

Calculating the p-value,

=P(Z>|−1.78|)=0.0375

Thus At 5%the null hypothesis gets rejected as the p-value is less and at 1%it is not rejected as p-value is greater.

03

Explanation Part (b)

The null and alternative hypotheses are,

H0:p=0.65Ha:p≠0.65

Calculating the p-value,

=2×P(Z>|Z|)

=2×0.0375=0.0750

Hence at the 5%significance level and at the 1%level the null hypothesis doesn't get rejected as the p-value is greater.

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