24. Use technology to help you test the claim about the population mean, , at th

Question

24. Use technology to help you test the claim about the population mean, , at the given level of significance, , using the given sample statistics. Assume the population is normally distributed.

Claim: > 1190; = 0.06; = 202.07. Sample statistics: x = 1222.56, n = 200

Identify the null and alternative hypotheses. Choose the correct answer below.

A

H0:1222.56

B

H0:>1222.56

Ha:>1222.56

Ha:1222.56

C

H0:1190

D

H0:1222.56

Ha:>1190

Ha:<1222.56

E

H0:1190

F

H0:>1190

Ha:<1190

Ha:1190

Calculate the standardized test statistic.

The standardized test statistic is ____ (Round to two decimal places as needed.)

Determine the P-value.

P = ____ (Round to three decimal places as needed.)

Determine the outcome and conclusion of the test.

(Reject or Fail to reject) H0. At the 6% significance level, there (is or is not) enough evidence to (reject or support) the claim.

A

H0:1222.56

B

H0:>1222.56

Ha:>1222.56

Ha:1222.56

C

H0:1190

D

H0:1222.56

Ha:>1190

Ha:<1222.56

E

H0:1190

F

H0:>1190

Ha:<1190

Ha:1190

Explanation / Answer

. Use technology to help you test the claim about the population mean, , at the given level of significance, , using the given sample statistics. Assume the population is normally distributed.

Claim: > 1190; = 0.06; = 202.07. Sample statistics: x = 1222.56, n = 200

Identify the null and alternative hypotheses. Choose the correct answer below.

A

H0:1222.56

B

H0:>1222.56

Ha:>1222.56

Ha:1222.56

C

H0:1190

D

H0:1222.56

Ha:>1190

Ha:<1222.56

E

H0:1190

F

H0:>1190

Ha:<1190

Ha:1190

Calculate the standardized test statistic.

The standardized test statistic is 2.28 (Round to two decimal places as needed.)

Determine the P-value.

P = 0.011 (Round to three decimal places as needed.)

Determine the outcome and conclusion of the test.

(Reject) H0. At the 6% significance level, there (is) enough evidence to (support) the claim.

Z Test of Hypothesis for the Mean

Data

Null Hypothesis                       m=

1190

Level of Significance

0.06

Population Standard Deviation

202.07

Sample Size

200

Sample Mean

1222.56

Intermediate Calculations

Standard Error of the Mean

14.2885

Z Test Statistic

2.2788

Upper-Tail Test

Upper Critical Value

1.5548

p-Value

0.0113

Reject the null hypothesis

A

H0:1222.56

B

H0:>1222.56

Ha:>1222.56

Ha:1222.56

C

H0:1190

D

H0:1222.56

Ha:>1190

Ha:<1222.56

E

H0:1190

F

H0:>1190

Ha:<1190

Ha:1190

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