Question

In a recent​ poll, 801 adults were asked to identify their favorite seat when they​ fly, and 476 of them chose a window seat. Use a 0.05 significance level to test the claim that the majority of adults prefer window seats when they fly. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution.

Which of the following is the hypothesis test to be​ conducted?

A.

Upper H 0 : p greater than 0.5H0: p>0.5

Upper H 1 : p equals 0.5H1: p=0.5

B.

Upper H 0 : p equals 0.5H0: p=0.5

Upper H 1 : p not equals 0.5H1: p≠0.5

C.

Upper H 0 : p not equals 0.5H0: p≠0.5

Upper H 1 : p equals 0.5H1: p=0.5

D.

Upper H 0 : p equals 0.5H0: p=0.5

Upper H 1 : p greater than 0.5H1: p>0.5

E.

Upper H 0 : p less than 0.5H0: p<0.5

Upper H 1 : p equals 0.5H1: p=0.5

F.

Upper H 0 : p equals 0.5H0: p=0.5

Upper H 1 : p less than 0.5H1: p<0.5

What is the test​ statistic?

z=___

​(Round to two decimal places as​ needed.)

What is the​ P-value?

​P-value = ___

​(Round to three decimal places as​ needed.)

What is the conclusion about the null​ hypothesis?

A.Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, α.

B.Reject the null hypothesis because the​ P-value is greater than the significance​ level, α.

C.Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, α.

D.Fail to reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, α.

What is the final​ conclusion?

A.There is not sufficient evidence to support the claim that the majority of adults prefer window seats when they fly.

B.There is sufficient evidence to support the claim that the majority of adults prefer window seats when they fly.

C.There is sufficient evidence to warrant rejection of the claim that the majority of adults prefer window seats when they fly.

D.There is not sufficient evidence to warrant rejection of the claim that the majority of adults prefer window seats when they fly.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

= x / n = 476 / 801 = 0.5943

P₀ = 0.5

1 - P₀ = 0.5

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5943 - 0.5 / [(0.5 * 0.5) / 801]

= 5.33

P(z > 5.33) = 1 - P(z < 5.33) = 0

P-value = 0

= 0.05

P-value <

A)Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, .

C)There is sufficient evidence to warrant rejection of the claim that the majority of adults prefer window seats when they fly.