Question

An important factor in selling a residential property is the number of times real estate, agents show a home. A sample of 21 homes recently sold in Buffalo, New York area revealed the mean number of times a home was shown was 23 and the standard deviation of the sample was 8 people.
What was the marginal error of a 99% confidence interval ?


What is the 99% confidence interval for the population mean ?

Answer 1

Using the t-distribution to build the 99% confidence interval, it is found that:

• The margin of error is of 3.64.

• The 99% confidence interval for the population mean is (19.36, 26.64).

What is a t-distribution confidence interval?

The confidence interval is:

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

In which:

• $\overline{x}$ is the sample mean.

• t is the critical value.

• n is the sample size.

• s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 21 - 1 = 20 df, is t = 2.086.

The other parameters are given as follows:

$\overline{x} = 23, s = 8, n = 21$

The margin of error is given by:

$M = t\frac{s}{\sqrt{n}} = 2.086\frac{8}{\sqrt{21}} = 3.64$

Hence the bounds of the interval are:

$\overline{x} - M = 23 - 3.64 = 19.36$

$\overline{x} + M = 23 + 3.64 = 26.64$

The 99% confidence interval for the population mean is (19.36, 26.64).

More can be learned about the t-distribution at brainly.com/question/16162795

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