# Question: In this exercise you are to perform a computer simulation

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).

**View Solution:**## Answer to relevant Questions

As we mentioned on page 403, the following relationship holds between hypothesis tests and confidence intervals: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ1 = μ2 will be ...Suppose that you want to perform a hypothesis test to compare the means of two populations, using independent simple random samples. Assume that the two distributions of the variable under consideration have the same shape, ...x1 = 20, s1 = 6, n1 = 20, . x2 = 24, s2 = 2, n2 = 15 a. Left-tailed test, α = 0.05 b. 90% confidence interval We have provided summary statistics for independent simple random samples from two populations. In each case, ...Refer to Exercise 10.71 and obtain a 90% confidence interval for the difference, μ1 − μ2, between the mean ages at arrest of East German prisoners with chronic PTSD and remitted PTSD. In Example 10.6 on page 411, we conducted a nonpooled t-test, at the 5% significance level, to decide whether the mean operative time is less with the dynamic system than with the static system. a. Using a pooled t-test, ...Post your question