You want to rent an unfurnished one-bedroom apartment in Dallas next year. The mean monthly rent for a random sample of 11 apartments advertised in the local newspaper is $1050. Assume the monthly rents in Dallas follow a Normal distribution with a standard deviation of $290. Find a 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.
(Round your answers to two decimal places.)
($_________ , $_______)
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.95 = mean ± Z(SD) = 1050 ± 290Z
Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportion/probability (±.025) and its Z score. Insert the Z score into the equation above to find your answers.
To find the 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments in Dallas, we can use the formula:
Confidence Interval = Sample mean ± Margin of Error
First, let's calculate the margin of error:
Margin of Error = Critical value × Standard error of the mean
The critical value can be found using the Z-table or Z-score calculator. Since we want a 95% confidence interval, the critical value is the Z-score associated with a 95% confidence level, which is 1.96.
The standard error of the mean can be calculated using the formula:
Standard error of the mean = Standard deviation / √n
where n is the sample size. In this case, the sample size is 11.
Let's calculate the margin of error:
Standard error of the mean = $290 / √11 ≈ $87.60
Margin of Error = 1.96 × $87.60 ≈ $171.58
Now, we can calculate the 95% confidence interval:
95% Confidence Interval = Sample mean ± Margin of Error
Since the sample mean is $1,050, the lower bound of the confidence interval is:
$1,050 - $171.58 ≈ $878.42
The upper bound of the confidence interval is:
$1,050 + $171.58 ≈ $1,221.58
Therefore, the 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments in Dallas is approximately ($878.42, $1,221.58).