Refer to Exercises 1 and 2. Using that context as an example, define in your own words what is meant by a sampling distribution of the sample mean.
Exercise 1
Refer to Exercise 2. If a different sample of 100 marathon runners was taken from the same population, which of the following would be the same as it was for the first sample, and which would be different? Explain your answer in each part.
a. The value of the mean of the sampling distribution of the sample mean.
b. The approximate shape of the sampling distribution of the sample mean.
c. The standard deviation of the sampling distribution of the sample mean.
Exercise 2
Researchers would like to know the mean body temperature of runners at the completion of a marathon. They plan to take a random sample of 100 runners who complete a marathon and record their temperatures. Which of the following will the researchers know after they have taken the sample? Explain your answer in each part.
a. The value of the mean of the sampling distribution of the sample mean.
b. The approximate shape of the sampling distribution of the sample mean.
c. The standard deviation of the sampling distribution of the sample mean.