3. On a stretch of interstate highway with a speed limit of 65 miles per hour, a

Question

3. On a stretch of interstate highway with a speed limit of 65 miles per hour, an unusual number of accidents were being reported. Forty-one cars were randomly checked and clocked for speed by the state police. The speeds are shown below 76 89 68 75 74 81 80 77 65 77 80 70 76 76 70 73 85 71 67 73 82 71 80 82 82 77 78 77 69 81 74 79 87 71 84 69 61 66 85 68 76 Anything above 73 miles per hour is considered excessive speed. Is there sufficient evidence for the police to conclude that there is excessive speeding on this stretch of highway? Conduct a hypothesis test using a significance level of = 0.05. Make sure to clearly identify your test statistic and explain what the P-value means in the context of the problem.

Explanation / Answer

Mean, x = 75.65854
s = 6.444415
n = 41

Ho: <= 73
Ha: > 73

Test statistic, t = (x - )/(s/sqrt(n)) = (75.65854 - 73)/(6.444415/sqrt(41)) = 2.64

Degree of freedom = n - 1 = 40

P-Value (One sided) = 0.0059 which is less than (<) 0.05(significance level)
P-value is the probability of obtaining a result at least as extreme as the one that was actually observed in the sample, given that the null hypothesis is true.

We can reject null hypothesis and can conclude the average speed is greater than 73 miles per hour

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