Question

In a random sample of 7 residents of the state of Maine, the mean waste recycled per person per day was 1.4 pounds with a standard deviation of 0.23 pounds.

a. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Maine. Assume the population is approximately normal.
b. Find the critical value that should be used in constructing the confidence interval.

Answer 1

a) The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.

b)
`T_c = 2.4469`

Explanation:

We have the standard deviation for the sample, which means that the t-distribution is used 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 = 7 - 1 = 6

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.95)/(2) = 0.975`. So we have T = 2.4469, and the answer to question b is
`T_c = 2.4469`

The margin of error is:

`M = T(s)/(√(n)) = 2.4469(0.23)/(√(7)) = 0.21`

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 1.4 - 0.21 = 1.19 pounds.

The upper end of the interval is the sample mean added to M. So it is 1.4 + 0.21 = 1.61 pounds.

The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.