You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a random sample of 14 apartments advertised in the local newspaper is $1200. Assume that the standard deviation is $230. Find a 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.
Answered in a subsequent post.
To find a 95% confidence interval for the mean monthly rent, we will use the formula:
Confidence Interval = sample mean ± (critical value * standard error)
First, let's determine the critical value. Since the sample size is less than 30, we will use a t-distribution instead of a normal distribution. We need to find the t-critical value with a confidence level of 95% and degrees of freedom equal to n - 1 (sample size minus 1).
Degrees of freedom = 14 - 1 = 13
Using a t-table or a calculator, we can find the t-critical value with a confidence level of 95% and 13 degrees of freedom. In this case, it is approximately 2.160.
Next, we need to calculate the standard error, which is the standard deviation divided by the square root of the sample size.
Standard error = standard deviation / √sample size
= $230 / √14
≈ $61.41
Now, we can calculate the confidence interval.
Confidence Interval = $1200 ± (2.160 * $61.41)
Lower bound = $1200 - (2.160 * $61.41)
≈ $1090.97
Upper bound = $1200 + (2.160 * $61.41)
≈ $1309.03
Therefore, the 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments in Boston is approximately $1090.97 to $1309.03.