Question

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

Answer 1

(a) C: 0.0465 ; reject the null hypothesis

(b) B: 0.3409 ; fail to reject the null hypothesis

Explanation:

Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

• If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.

• If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.

(a) Now, we are given alternate hypothesis,
`H_1` : p < 3/5

Also, 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
`\leq` 1.68)

= 1 - 0.95352 = 0.0465

Since, 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,
`H_1` : p > 0.383

Also, 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
`\leq` 0.41)

= 1 - 0.6591 = 0.3409

Since, 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.