Question

In a random sample of 11 residents of the state of New York, the mean waste recycled per person per day was 2.9 pounds with a standard deviation of 0.98 pounds. Determine the 80% confidence interval for the mean waste recycled per person per day for the population of New York. Assume the population is approximately normal. Step 2 of 2 : Construct the 80% confidence interval. Round your answer to one decimal place.

Answer 1

The 80% confidence interval for the mean waste recycled per person per day for the population of New York is between 1.6 pounds and 4.2 pounds

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 = 11 - 1 = 10

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 10 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.8)/(2) = 0.9`. So we have T = 1.372

The margin of error is:

M = T*s = 1.372*0.98 = 1.3

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 2.9 - 1.3 = 1.6 pounds

The upper end of the interval is the sample mean added to M. So it is 2.9 + 1.3 = 4.2 pounds

The 80% confidence interval for the mean waste recycled per person per day for the population of New York is between 1.6 pounds and 4.2 pounds