To solve this problem, we need to compare the mean 5-year capitalization rate of retail tenants with low S&P ratings (BBB-) to the mean for tenants with high S&P ratings (A, M-, or M).
a. First, we need to calculate the mean 5-year capitalization rate for the low S&P rating tenants. Add up the capitalization rates for the low S&P rating tenants and divide by the number of tenants in that group (5 tenants in this case):
Mean for low S&P rating tenants = (8.254 + 8.448 + 7.496 + 8.497 + 8.501) / 5
b. Next, calculate the mean 5-year capitalization rate for the high S&P rating tenants. Add up the capitalization rates for the high S&P rating tenants and divide by the number of tenants in that group (8 tenants in this case):
Mean for high S&P rating tenants = (6.745 + 6.753 + 5.499) / 3
c. Now, we need to find the standard deviation for each group. To do this, we'll use the formula for sample standard deviation:
Standard deviation for low S&P rating tenants = sqrt(((8.254 - mean)^2 + (8.448 - mean)^2 + (7.496 - mean)^2 + (8.497 - mean)^2 + (8.501 - mean)^2) / (5 - 1))
Standard deviation for high S&P rating tenants = sqrt(((6.745 - mean)^2 + (6.753 - mean)^2 + (5.499 - mean)^2) / (3 - 1))
d. Calculate the standard error for each group. The standard error is the standard deviation divided by the square root of the sample size:
Standard error for low S&P rating tenants = standard deviation for low S&P rating tenants / sqrt(5)
Standard error for high S&P rating tenants = standard deviation for high S&P rating tenants / sqrt(3)
e. Calculate the t-statistic using the formula:
t = (mean for low S&P rating tenants - mean for high S&P rating tenants) / sqrt((standard error for low S&P rating tenants)^2 + (standard error for high S&P rating tenants)^2)
f. Finally, compare the t-statistic to the critical value from the t-distribution table with (n1 + n2 - 2) degrees of freedom, where n1 and n2 are the sample sizes of the two groups. If the t-statistic is greater than the critical value, we can conclude that there is a significant difference between the mean capitalization rates of the two groups.
Note: The steps provided above assume that the data is accurate and there are no errors in the given information.