Hypothesis Testing - Means (7.3)

3) Test the following claims showing all 4 steps of your hypothesis test. Be sure to define all variables before stating your hypotheses

1. 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 alpha = 0.05? This needs to be done problem completely by hand using the Standard Normal Table.
3. According to a study, the mean cost of bariatric (weight loss) surgery is $21,500. You think this information is incorrect. You randomly select 25 bariatric surgery patients and find that the mean cost for their surgeries is $20,695. From past studies, the population standard deviation is known to be $2250 and the population is normally distributed. Is there enough evidence to support your claim at a = 0.05?
5. An article titled "Teen Boys Forget Whatever It Was" appeared in the Australian newspaper The Mercury (April 21, 1997). It described a study of academic performance and attention span and reported that the mean time to distraction for teenage boys working on an independent task is 4 minutes. Although the sample size wasn't given in the article, suppose that this mean was based on a random sample of 50 teenage boys and the sample standard deviation was 1.4 minutes.Is there convincing evidence that the average attention span for teenage boys is less than 5 minutes? Test the relevant hypotheses using alpha = 0.01.