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 7.37 (p. 317). 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?
Exercise 7.37
Duration of daylight in western Pennsylvania. What area of the United States has the least amount of daylight, on average? Having grown up in western Pennsylvania, co-author Sincich wonders if it is his hometown of Sharon, PA. Data on the number of minutes of daylight per day in Sharon, PA, for 12 randomly selected days (one each month) in 2009 were obtained from the Naval Oceanography Portal Web site (aa.usno.navy.mil/USNO/astronomical-applications/ data-services). The data are listed in the table and saved in the DAYLIGHT file. Descriptive statistics and a 95% confidence interval for the mean are produced in the SPSS printout on page 318.
a. Locate the confidence interval on the printout and give the value of the confidence coefficient.
b. Use the descriptive statistics on the printout to calculate the 95% confidence interval. Be sure your answer agrees with the interval shown on the printout.
c. Practically interpret the confidence interval.
d. Comment on the method of sampling. Do you think the sample is representative of the target population?
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