## use the given information to find the p-value. also use a0.05 significance level and state the conclusion about the null hypothesis (reject

use the given information to find the p-value. also use a0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail tor rejected the null hypothesis)

With H1 : p < 3/5; the test statistic is z = -1.68

A: 0.093 ; fail to reject the null hypothesis

B: 0.0465 ; fail to reject the null hypothesis

C: 0.0465 ; reject the null hypothesis

D: 0.09535 ; fail to reject the null hypothesis

With H1 : p > 0.383, the test statistic is z = 0.41

A: 0.6591 ; fail to reject the null hypothesis

B: 0.3409 ; fail to reject the null hypothesis

C: 0.3490 ; reject the null hypothesis

D: 0.6818 ; reject the null hypothesis

## Answers ( )

Answer:(a) C: 0.0465 ; reject the null hypothesis(b) B: 0.3409 ; fail to reject the null hypothesisStep-by-step explanation:Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

(a)Now, we are given alternate hypothesis, : p < 3/5Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;

P-value = P(Z < -1.68) = 1 – P(Z 1.68)

= 1 – 0.95352 =

0.0465Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which

we reject the null hypothesis.(b)Now, we are given alternate hypothesis, : p > 0.383Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;

P-value = P(Z > 0.41) = 1 – P(Z 0.41)

= 1 – 0.6591 =

0.3409Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which

we fail to reject the null hypothesis.