84 Duration of daylight in western Pennsylvania. Refer to the Naval Oceanography Portal data on number of minutes of daylight per day in Sharon, PA, Exercise 37 . An estimate of the mean number of minutes of daylight per day was obtained using data collected for 12 randomly selected days (one each month) in 2009.

a. Determine the number of days in 2009 that need to be sampled in order to estimate the desired mean to within 45 minutes of its true value with 95% confidence.

b. Based on your answer, part a , develop a sampling plan that will likely result in a random sample that is representative of the population.

c. Go to the Web site, http://aa.usno.navy.mil/USNO/

astronomical-applications/data-services , and collect the data for Sharon, PA in year 2009 using your sampling plan.

d. Use the data, part c , to construct a 95% confidence interval for the desired mean. Does your interval have the desired width?