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

Question

a county is considering raising the speed limit on the 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 5.1 miles per hour. At a=0.10, do you have enough evidence to support the county's claim?
a) calculate the standardized test.
t=
(round to 2 decimal places as needed)

b) decide whether to reject or fail to reject the null hypothesis. if the P-value is less than the level of significance, reject the null hypothesis. otherwise , fail to reject the null hypothesis

c) interprete the decision in the Context of the original claim . if the null hypothesis is rejected then there is sufficient evidence to support the county's claim that the mean speed of vehicles is greater than the posted speed limit. if the null hypothesis is rejected then there is not sufficient evidence to support the claim that the mean vehicle speed is greater than the posted speed limit.

Explanation / Answer

a)Z = (x-mean)/[sigma/sqrt(n)] = (49-45)/[5.1/sqrt(25)] = 3.92

b)For z=3.92 in a one-sided test, we have p-value equal to 0.000044 from normal tables.

Since p-value is less than 0.10, we reject the null hypothesis

c) Rejecting the null hypothesis means that there is sufficient evidence to support the county's claim that the mean speed of vehicles is greater than the posted speed limit

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