Homeowners claim that the mean speed of automobiles traveling on their street is greater than the speed limit of 35 miles per hour. A random sample of 100 automobiles has a mean speed of 36 miles per hour. Assume the population standard deviation is 4 miles per hour. Is there enough evidence to support the claim at α = 0.05? Use a P-value.
a. Identify the claim. Then state the null and alternative hypotheses.
b. Identify the level of significance α.
c. Find the standardized test statistic z.
d. Find the P-value.
e. Decide whether to reject the null hypothesis.
f. Interpret the decision in the context of the original claim.