When we work with quantitative data with a population mean of , we have to modif

Question

When we work with quantitative data with a population mean of , we have to modify our sampling distribution model. Two issues come up 1. Most important, we do not usually know what the true value of (the population standard deviation) is, so we know the normal distribution will not be the correct sampling distribution model. We use s (the standard deviation of the sample) instead. To correct for the fact that a calc ulation of s also uses sample information (y) we don't use the sample size (n) when we go to the t-table. Instead, we use n-1. "n-1" is called the "degrees of freedom", or the number of pieces of ind ependent information in the sample that can be used to find the sampling distribution model. (There are exceptions: for example, human heights, temperature, human weights, and so forth) 2. In addition, we know for smaller samples, the area of the tail of the distribution that is associated with a particular critic al value is larger (a "fat tail). So the critical value of 1.96 standard deviations above the mean (z-1.96) for a normal distribution has 2.5% as the area of the "right" tail. For a t-distribution with a sample size of 20 (and degrees of freedom of 19), the area is 6.48% 3. The data in the sample should be "nearly normal". For a sample size of 15-40, the histogram should be symmetric and unimodal I am trying to find out the average tread life of tires manufactured by the Toyo tire company. I take a random sample of 36 tires that have worn out. The sample includes information on how long the tires lasted. y from the sample is 32,000 miles and the standard deviation in the sample is 3,000 miles. What is the appropriate sampling distribution model for this sample information? [You may assume that the histogram is symmetric and unimodal) Select one a, y-N(32000.3000) b. y N(32000,3000/6) c. y-t35(u,3000/6) d. y-t(3000/6)

Explanation / Answer

Te unimodal ddistribution is one where there is one clear peak. This is with the case with the normal distribution.

Thus the coreect opyion is (A).

ybar ~N(32000.3000)

ybar is normally distributed with mean 36000 and standard deviation 3000.

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