# Question: In the paper Cloudiness Note on a Novel Case of

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?

**View Solution:**## Answer to relevant Questions

One-Sided One-Mean t-Intervals. Presuming that the assumptions for a one-mean t-interval are satisfied, we have the following formulas for (1 − α)-level confidence bounds for a population mean μ: Lower confidence bound: ...Refer to Examples 8.1 and 8.2. Use the data in Table 8.1 on page 305 to obtain a 68.26% confidence interval for the mean price of all new mobile homes. (Proceed as in Example 8.2, but use the "68.26" part of the ...Suppose that you have obtained data by taking a random sample from a population. Before performing a statistical inference, what should you do? Data on investments in the high-tech industry by venture capitalists are compiled by Venture One Corporation and published in America's Network Telecom Investor Supplement. A random sample of 18 venture capital investments ...According to the document All About Diabetes, found on the Web site of the American Diabetes Association, ". . .diabetes is a disease in which the body does not produce or properly use insulin, a hormone that is needed to ...Post your question