A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 45 miles per hour. A random sample of 25 vehicles has a mean speed of 49 miles per hour and a standard deviation of 4.8 miles per hour. At =0.01, do you have enough evidence to support thecounty's claim? Complete parts(a) through(d) below.

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(a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.

A.H0: 45

Ha: <45

B.H0: 45

Ha: =45

C.H0: 45

Ha: >45

D.H0: =45

Ha: 45

(b) Calculate the standardized test statistic.

t=____

(Round to two decimal places asneeded.)

Use technology to calculate theP-value.

P-value=_____

(Round to three decimal places asneeded.)

(c) Decide whether to reject or fail to reject the null hypothesis.

A. Reject H0 because theP-value islessthan the significancelevel, 0.01.

B. Failtoreject H0 because theP-value isgreaterthan the significancelevel, 0.01.

C. Failtoreject H0 because theP-value islessthan the significancelevel, 0.01.

D. Reject H0 because theP-value isgreaterthan the significancelevel, 0.01.

(d) Interpret the decision in the context of the original claim.

A. There isnot sufficient evidence to support thecounty's claim that the mean speed of vehicles is greater than 45 miles per hour.

B. There is sufficient evidence to support thecounty's claim that the mean speed of vehicles is less than 45 miles per hour.

C. There is sufficient evidence to support thecounty's claim that the mean speed of vehicles is greater than 45 miles per hour.

D. There isnot sufficient evidence to support thecounty's claim that the mean speed of vehicles is less than 45 miles per hour.