# Question

In this exercise, you are to perform a computer simulation to illustrate the distribution of the pooled t-statistic, given in Key Fact 10.2 on page 397.

a. Simulate 1000 random samples of size 4 from a normally distributed variable with a mean of 100 and a standard deviation of 16. Then obtain the sample mean and sample standard deviation of each of the 1000 samples.

b. Simulate 1000 random samples of size 3 from a normally distributed variable with a mean of 110 and a standard deviation of 16. Then obtain the sample mean and sample standard deviation of each of the 1000 samples.

c. Determine the value of the pooled t-statistic for each of the 1000 pairs of samples obtained in parts (a) and (b).

d. Obtain a histogram of the 1000 values found in part (c).

e. Theoretically, what is the distribution of all possible values of the pooled t-statistic?

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

a. Simulate 1000 random samples of size 4 from a normally distributed variable with a mean of 100 and a standard deviation of 16. Then obtain the sample mean and sample standard deviation of each of the 1000 samples.

b. Simulate 1000 random samples of size 3 from a normally distributed variable with a mean of 110 and a standard deviation of 16. Then obtain the sample mean and sample standard deviation of each of the 1000 samples.

c. Determine the value of the pooled t-statistic for each of the 1000 pairs of samples obtained in parts (a) and (b).

d. Obtain a histogram of the 1000 values found in part (c).

e. Theoretically, what is the distribution of all possible values of the pooled t-statistic?

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

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