Question

Identify the P-VALUE in a hypothesis test of the following claim and sample data: Claim: "The average annual household income in Warren County is $47,500." A random sample of 86 households from this county is obtained, and they have an average annual income of $48,061 with a standard deviation of $2,351. Test the claim at the 0.02 significance level.

a. 0.013
b. 0.015
c. 0.030
d. 0.027

Identify the CONCLUSION of a hypothesis test of the following claim and sample data: Claim: "The average annual household income in Warren County is $47,500." A random sample of 86 households from this county is obtained, and they have an average annual income of $48,061 with a standard deviation of $2,351. Test the claim at the 0.02 significance level.

a. There is not sufficient evidence to warrant rejection of the claim.
b. There is sufficient evidence to support the claim.
c. There is not sufficient evidence to support the claim.
d. There is sufficient evidence to warrant rejection of the claim.

Answer 1

(a)

SE = s/

= 2351/ = 253.5154

Test statistic is:
Z = ( - )/SE

= (48061 - 47500)/253.5154 = 2.2129

Table of Area Under Standard Normal Curve gives area = 0.4864

So,

P-value = (0.5 - 0.4864) X 2 = 0.0272

(b)

= 0.02

Since P-value = 0.0272 is greater than = 0.02, Fail to reject H0.

Conclusion:
Correct option:

a. There is not sufficient evidence to warrent rejection of the claim.