An investor wants to determine the true average yield on a selection of investments from the Business week 1000. Suppose the investor draws a random sample of (n=40 firms) and finds an average yield on investment of (xbar = 5.00%) and a sample standard deviation (s = 1.50%). Construct a 95% confidence interval for the true average yield, using (s) as an estimate for the population standard deviation.

To construct a 95% confidence interval for the true average yield, we can use the formula:

Confidence Interval = xbar ± (t * (s / √n))

Here, xbar represents the sample mean (5.00%), s represents the sample standard deviation (1.50%), n represents the sample size (40), and t represents the critical value from the t-distribution at a confidence level of 95%.

To find the critical value, we need to determine the degrees of freedom (df), which is given by (n - 1). So in this case, df = (40 - 1) = 39.

Next, we need to find the t-value associated with a 95% confidence level and 39 degrees of freedom. This can be done using a t-table or a statistical calculator. For simplicity, let's assume the t-value is approximately 2.0227.

Now we can substitute these values into the formula:

Confidence Interval = 5.00% ± (2.0227 * (1.50% / √40))

Calculating the values within the parentheses first:

Confidence Interval = 5.00% ± (2.0227 * 0.2387)

Finally, calculate the confidence interval:

Upper Limit = 5.00% + (2.0227 * 0.2387) = 5.4829% (rounded to four decimal places)
Lower Limit = 5.00% - (2.0227 * 0.2387) = 4.5171% (rounded to four decimal places)

Therefore, the 95% confidence interval for the true average yield on the selection of investments is approximately between 4.5171% and 5.4829%.