For these exercises, perform each of these steps. Assume that all variables are normally or approximately normally distributed.
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified and assume the variances are unequal.

Find the 95% confidence interval for the difference of the means in Exercise 3 of this section.

Data from in Exercise 3

The mean noise level of 20 randomly selected areas designated as “casualty doors” was 63.1 dBA, and the sample standard deviation is 4.1 dBA. The mean noise level for 24 randomly selected areas designated as operating theaters was 56.3 dBA, and the sample standard deviation was 7.5 dBA. At α = 0.05, can it be concluded that there is a difference in the means?