# Question: An issue of Scientific American revealed that the batting averages

An issue of Scientific American revealed that the batting averages of major-league baseball players are normally distributed with mean .270 and standard deviation .031.

a. Simulate 2000 samples of five batting averages each.

b. Determine the sample mean and sample standard deviation of each of the 2000 samples.

c. For each of the 2000 samples, determine the observed value of the standardized version of x-bar.

d. Obtain a histogram of the 2000 observations in part (c).

e. Theoretically, what is the distribution of the standardized version of x-bar?

f. Compare your results from parts (d) and (e).

g. For each of the 2000 samples, determine the observed value of the studentized version of x-bar.

h. Obtain a histogram of the 2000 observations in part (g).

i. Theoretically, what is the distribution of the studentized version of x-bar?

j. Compare your results from parts (h) and (i).

k. Compare your histograms from parts (d) and (h). How and why do they differ?

a. Simulate 2000 samples of five batting averages each.

b. Determine the sample mean and sample standard deviation of each of the 2000 samples.

c. For each of the 2000 samples, determine the observed value of the standardized version of x-bar.

d. Obtain a histogram of the 2000 observations in part (c).

e. Theoretically, what is the distribution of the standardized version of x-bar?

f. Compare your results from parts (d) and (e).

g. For each of the 2000 samples, determine the observed value of the studentized version of x-bar.

h. Obtain a histogram of the 2000 observations in part (g).

i. Theoretically, what is the distribution of the studentized version of x-bar?

j. Compare your results from parts (h) and (i).

k. Compare your histograms from parts (d) and (h). How and why do they differ?

## Answer to relevant Questions

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 ...In a poll of 1009 U.S. adults of age 18 years and older, conducted December 4–7, 2008, Gallup asked “Roughly how much money do you think you personally will spend on Christmas gifts this year?”. The data provided on ...In each part, assume that the population standard deviation is known. Decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers. a. The sample ...x-bar = 55, n = 16, σ = 5, confidence level = 99% We provide a sample mean, sample size, population standard deviation, and confidence level. In each case, use the one-mean z-interval procedure to find a confidence interval ...The Bureau of Justice Statistics provides information on prison sentences in the document National Corrections Reporting Program. A random sample of 20 maximum sentences for murder yielded the data, in months, presented on ...Post your question