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

Solution:

Given:

Significance level  = 0.05

Part a)

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

Since H1 is < type, this is left tailed test.

Thus for left tailed test , p-value is:

p-value = P(Z < z test statistic)

p-value = P(Z < -1.68)

Look in z table for z = -1.6 and 0.08 and find corresponding area.

P( Z<-1.68) = 0.0465

p-value = P(Z < -1.68)

p-value = 0.0465

Decision Rule:
Reject null hypothesis H0, if p-value < 0.05 level of significance, otherwise we fail to reject H0

Since p-value = 0.0465 < 0.05 level of significance, we reject null hypothesis H0.

Thus correct answer is:

C: 0.0465 ; reject the null hypothesis

Part b)

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

Since H1 is > type , this is right tailed test.

For right tailed test , p-value is:

p-value = P(Z > z test statistic)

p-value = P(Z > 0.41)

p-value = 1 - P(Z < 0.41)

Look in z table for z = 0.4 and 0.01 and find corresponding area.

P( Z < 0.41) = 0.6591

thus

p-value = 1 - P(Z < 0.41)

p-value = 1 -0.6591

p-value = 0.3409

Since p-value = 0.3409 >  0.05 level of significance, we fail to reject H0.

Thus correct answer is:

B: 0.3409 ; fail to reject the null hypothesis