Question

The speed limit on the highway in LA was raised to 75 mph. The speed of 121 cars that passed the checkpoint was collected. It was found that the speed of the cars collected was 78 mph and the standard deviation of 4 mph. Conduct a hypothesis at alpha= 0.01 level of significance to see if this is enough evidence to show that drivers are still speeding (over 75 mph) on the highway.

A: Write a hypothesis.

Ho: U=75

H1: U>75

B: Perform the test using either the critical value method or p-value method

78-75/(4/√121)= 8.25

Is this correct? I am having a really hard time getting through this point to find the answer either through p-value method or critical value method.

Answer 1

given data are:-

sample mean () = 78

sample sd(s) = 4

sample size (n) = 121

a).hypothesis:-

(claim)

b).the test statistic is :-

[YES. you had done correct!!!]

df = (n-1) = (121-1) = 120

t critical value for df= 120,alpha = 0.01,right (one) tailed test is:-

[ using t distribution table ]

decision rule :-

reject the null hypothesis if,

decision and conclusion:-

Reject H₀. There is enough evidence to show that drivers are still speeding (over 75 mph) on the highway at 0.01 level of significance.

[

so, we reject the null hypothesis.]

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