SOLUTION: An important factor in selling a residential property is the number of people who look through the home. A sample of 11 homes recently sold in the Halifax, Nova Scotia, area reveal

Question 1206798: An important factor in selling a residential property is the number of people who look through the home. A sample of 11 homes recently sold in the Halifax, Nova Scotia, area revealed the mean number looking through each home was 17 and the standard deviation of the sample was 3 people. Develop a 90% confidence interval for the population mean. (Round the final answers to 2 decimal places.)

Confidence interval for the population mean is between
and
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

mu = population mean = unknown
sigma = population standard deviation = unknown
xbar = 17 = sample mean
s = 3 = sample standard deviation
n = 11 = sample size

Since we do not know the population standard deviation (sigma), and because n > 30 is not the case, we must use the T distribution.
df = degrees of freedom
df = n-1
df = 11-1
df = 10

At 90% confidence, and df = 10, the t critical value is roughly t =1.812

You can use a table such as this
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
to determine the t critical value.
Highlight the row that has df = 10. Highlight the column that has "90%" at the bottom.
This row and column combo yields the value 1.812 which is approximate.

What this means is that P(-1.812 < t < 1.812) = 0.90 approximately when df = 10.

Another way to determine this t critical value is to use a stats calculator such as a TI84.
The specific function to use on a TI84 is called invT.
There are many other calculators that offer a similar feature.

--------------------------------------------------------------------------

Here are the important values we need
t = 1.812 (approximate)
xbar = 17
s = 3
n = 11

Then,
E = margin of error
E = t*s/sqrt(n)
E = 1.812*3/sqrt(11)
E = 1.639016 approximately

L = lower bound of confidence interval
L = xbar - E
L = 17 - 1.639016
L = 15.360984
L = 15.36

U = upper bound of confidence interval
U = xbar + E
U = 17 + 1.639016
U = 18.639016
U = 18.64

The 90% confidence interval of the format (L, U) is roughly (15.36, 18.64)
This represents 15.36 < mu < 18.64 which is a more descriptive way of explaining what's going on (since it involves the parameter we're trying to estimate).

We are 90% confident that the population mean (mu) is somewhere between 15.36 and 18.64

RELATED QUESTIONS
An important factor in selling a residential property is the number of people who look... (answered by stanbon)

An important factor in selling a residential property is the number of people who look... (answered by fcabanski)

In a sample of 1000 people,630 said they were most likely to sleep when at home sick with (answered by Boreal)

Residential customers who heat their home with natural gas have their monthly bills... (answered by Theo)

A realtor who is paid 7% of the selling price in commission recently received $10,794 in... (answered by mananth)

A realtor who is paid 8% of the selling price in commission recently received $10,794 (answered by checkley79)

A research company wishes to estimate, with 95% confidence, the proportion of people who... (answered by stanbon)

Surveyors asked a random sample of women in a major city what factor was the most... (answered by ewatrrr,Boreal)

1) The probability that a person is immune to a certain disease is 0.40. a)what is the... (answered by ewatrrr)