An important factor in selling a residential property is the number of people who look through the home. A sample of 21 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 25 and the standard deviation of the sample was 7 people.
Develop a 99% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced from a statistical model with a 95% confidence interval of 9.50 - 10.50.

Given:

Sample size = 21

Mean = 25

Standard deviation = 7

Confidence interval = 99%

α=1−0.99=0.01

α/2 = 0.005

Degrees of freedom(df)=n−1=21−1=20

Critical value(tc)=tα/2,df = t0.005,20 = 2.8433

Confidence Interval = mean +- tc * s/[tex]\sqrt{n}[/tex]

C.I = 25 ± 2.8433×7/[tex]\sqrt{21}[/tex]

C.I = (25 ± 4.3432)

C.I = (25−4.3432, 25+4.3432)

C.I = (20.6568, 29.3432)

99% confidence interval for the population average of the times homes are shown is (20.6568, 29.3432)

Learn more about confidence intervals:

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