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Tema [17]
2 years ago
12

An important factor in selling a residential property is the number of times real estate agents show a home. A sample of 23 home

s 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.
a. What is the margin of error for a 98% confidence interval?

b.What is the 98% confidence interval for the population mean?
Mathematics
1 answer:
yanalaym [24]2 years ago
3 0

Using the t-distribution, it is found that:

a. The <u>margin of error</u> is of 4.7 homes.

b. The 98% confidence interval for the population mean is (19.3, 28.7).

The information given in the text is:

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

We are given the <u>standard deviation for the sample</u>, which is why the t-distribution is used to solve this question.

The confidence interval is:

\overline{x} \pm M

The margin of error is:

M = t\frac{s}{\sqrt{n}}

Item a:

The critical value, using a t-distribution calculator, for a two-tailed <u>98% confidence interval</u>, with 23 - 1 = <u>22 df</u>, is t = 2.508.

Then, the <em>margin of error</em> is:

M = t\frac{s}{\sqrt{n}} = 2.508\frac{9}{\sqrt{23}} = 4.7

Item b:

The interval is:

\overline{x} - M = 24 - 4.7 = 19.3

\overline{x} + M = 24 + 4.7 = 28.7

The 98% confidence interval for the population mean is (19.3, 28.7).

A similar problem is given at brainly.com/question/15180581

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