# Question

In the paper "Cloudiness: Note on a Novel Case of Frequency" (Proceedings of the Royal Society of London, Vol. 62, pp. 287-290), K. Pearson examined data on daily degree of cloudiness, on a scale of 0 to 10, at Breslau (Wroclaw), Poland, during the decade 1876-1885. A frequency distribution of the data is presented in the following table.

Consider the days in the decade in question a population of interest, and let the variable under consideration be degree of cloudiness in Breslau.

a. Determine the population mean, μ, that is, the mean degree of cloudiness. (Hint: Multiply each degree of cloudiness in the table by its frequency, sum the products, and then divide by the total number of days.)

b. Suppose we take a simple random sample of size 10 from the population with the intention of finding a 95% confidence interval for the mean degree of cloudiness (although we actually know that mean). Would use of the one-mean t-interval procedure be appropriate? Explain your answer.

c. Simulate 150 degrees-of-cloudiness observations.

d. Use your data from part (c) and the one-mean t-interval procedure to find a 95% confidence interval for the mean degree of cloudiness.

e. Does the population mean, μ, lie in the confidence interval that you found in part (d)?

f. If you answered "yes" in part (e), would your answer necessarily have been that?

Consider the days in the decade in question a population of interest, and let the variable under consideration be degree of cloudiness in Breslau.

a. Determine the population mean, μ, that is, the mean degree of cloudiness. (Hint: Multiply each degree of cloudiness in the table by its frequency, sum the products, and then divide by the total number of days.)

b. Suppose we take a simple random sample of size 10 from the population with the intention of finding a 95% confidence interval for the mean degree of cloudiness (although we actually know that mean). Would use of the one-mean t-interval procedure be appropriate? Explain your answer.

c. Simulate 150 degrees-of-cloudiness observations.

d. Use your data from part (c) and the one-mean t-interval procedure to find a 95% confidence interval for the mean degree of cloudiness.

e. Does the population mean, μ, lie in the confidence interval that you found in part (d)?

f. If you answered "yes" in part (e), would your answer necessarily have been that?

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