Question

An important factor in selling a residential property is the number of times real estate agents show a home. A sample of 23 homes recently sold in the Buffalo, New York, area revealed the mean number of times a home was shown was 24 and the standard deviation of the sample was 9 people.

Answer 1

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 standard deviation for the sample, hence the t-distribution is used to build the confidence interval. Important information are given by:

• Sample mean of $\overline{x} = 24$.
• Sample standard deviation of $s = 9$.
• Sample size of $n = 23$

The confidence interval is:

$\overline{x} \pm t\frac{s}{\sqrt{n}}$

In which t is the critical value for a 95% confidence interval with 23 - 1 = 22 df, thus, looking at a calculator or at the t-table, it is found that t = 2.0739.

Then:

$\overline{x} - t\frac{s}{\sqrt{n}} = 24 - 2.0739\frac{9}{\sqrt{23}} = 20.1$

$\overline{x} + t\frac{s}{\sqrt{n}} = 24 + 2.0739\frac{9}{\sqrt{23}} = 27.9$

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