The sampling distribution of a statistic is the distribution of values taken by

Question

The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. Example 2: During World War IlI, 12,000 able-bodied male undergraduates at the University of linois participated in required physical training. Each student ran a timed mile. Their times followed a normal distribution with mean 7.11 minutes and standard deviation 0.74 minutes. A random sample of 100 of these students has mean time -7.15 minutes. A second random sample of size 100 has meanx 6.97 minutes. After many random samples, the values of the many samples means () follow the normal distribution with mean 7.11 minutes and standard deviation 0.074 minutes. What is the population being described above? Describe the population distribution. How can one interpret that population mean and standard deviation in the context of this problem? a. aste Double Pockets200 Sheets oflege Ruled ROARING SPRING PAPER PROO

Explanation / Answer

a) The population here is able bodied male ungraduates at the university of illinois who participted in the physical training.

b) Population Distribution is normal

c) Mean = 7.11

SD = 0.74

This means that on average each student ran for 7.11 minutes. Basically, a small standard deviationmeans that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average.

So, SD is small here. Means that values of students' times are close to mean.

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