Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)
Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)
Use the Unit Circle to evaluate tan (π/4) = 1
Use Pythagorean Identity: cos²A + sin²A = 1
<u>Proof LHS → RHS</u>
= cos A
LHS = RHS: cos A = cos A
Using the t-distribution, it is found that the 95% confidence interval for the mean number of people the houses were shown is (20.1, 27.9).
We have the <u>standard deviation for the sample</u>, hence the t-distribution is used to build the confidence interval. Important information are given by:
The confidence interval is:
In which t is the critical value for a <u>95% confidence interval with 23 - 1 = 22 df</u>, thus, looking at a calculator or at the t-table, it is found that t = 2.0739.
Then:
The 95% confidence interval for the mean number of people the houses were shown is (20.1, 27.9).
A similar problem is given at brainly.com/question/15180581