Adele and Jessica live in different states and disagree about who has the higher electric bills. To settle their disagreement, the girls decide to sample electric bills in their area for the month of July and perform a hypothesis test. The electric company in Adele’s state reports that a random sample of 51 monthly residential electric bills has a mean of $87.63. Assume that the population standard deviation in Adele's state is known to be $22.98. For a random sample of 35 monthly residential electric bills in Jessica's state, the mean is $84.22. Assume that the population standard deviation in Jessica's state is $21.45. Is there evidence at the 0.01
level to say that the mean monthly residential electric bill is higher for Adele’s state than for Jessica’s state?
Find the P
-value for the hypothesis test. Round your answer to four decimal places.
b. Is there sufficient evidence to conclude that the mean monthly residential electric bill is higher for Adele's state than for Jessica's state? Test the claim at the 0.01 level of significance.