Question

to estimate the average monthly rent for 1 bedroom apartments, 13 complexes were randomly selected in Orlando. The mean cost is $970 with a standard deviation of $72. Find a 90% confidence interval for the mean monthly rent of all 1 bedroom apartments.

Answer 1

Answer:

The 90% confidence interval for the mean monthly rent of all 1 bedroom apartments is between $841.67 and $1098.33

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 13 - 1 = 12

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 12 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.9}{2} = 0.95$. So we have T = 1.7823

The margin of error is:

M = T*s = 1.7823*72 = 128.33

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 970 - 128.33 = $841.67

The upper end of the interval is the sample mean added to M. So it is 970 + 128.33 = $1098.33

The 90% confidence interval for the mean monthly rent of all 1 bedroom apartments is between $841.67 and $1098.33