A county is considering raising the speed limit on a road because they claim tha

Question

A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 40 miles per hour. A random sample of 20 vehicles has a mean speed of 45 miles per hour and a standard deviation of 4.4 miles per hour. At alpha = 0.01, do you have enough evidence to support the county's claim? Complete parts (a) through (d) below. Write the claim mathematically and identify H_0 and H_a. Choose the correct answer below. H_0: mu notequalto 40 H_a: mu = 40 H_0: mu = greaterthanorequalto 40 H_a: mu 40 H_0: mu = 40 H_a: mu notequalto 40 Calculate the standardized test statistic. t = (Round to two decimal places as needed.) Use technology to calculate the P-value. P-value = (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis. Fail to reject H_0 because the P-value is less than the significance level, 0.01. Reject H_0 because the P-value is less than the significance level, 0.01. Fail to reject H_0 because the P-value is greater than the significance level, 0.01. Reject H_0 because the p-value is greater than the significance level, 0.01. Interpret the decision in the context of the original claim. There is not sufficient evidence to support the county's claim that the mean speed of vehicles is less than 40 miles per hour. There is sufficient evidence to support the county's claim that the mean speed of vehicles is greater than 40 miles per hour. There is not sufficient evidence to support the county's claim that the mean speed of vehicles is greater than 40 miles per hour. There is sufficient evidence to support the county's claim that the mean speed of vehicles is less than 40 miles per hour.

Explanation / Answer

a.The research claim in the question is what will go in the alternate hypothesis
C is the right option
Ho: Mu<=40
Ha: Mu> 40

b. The test statistic is :
t = (45-40)/(4.4/sqrt(20)) = +5.08

P value is The P-Value is .000033.

The result is significant at p < .01

c. We reject null hypothesis as the p<.01
option B is right

d. B is the right interpretation of the result

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