The 95% confidence interval for the mean waste recycled per person per day for the population of Tennessee is (0.86, 1.74) pounds.
The critical value that should be used in constructing the 95% confidence interval is 2.100.
We know the sample size is 19 and the sample mean is 1.3 pounds.
We also know the sample standard deviation is 0.91 pounds.
We want to find the 95% confidence interval, which means we need to find the critical value that leaves 2.5% of the area in each tail of the t-distribution.
With 18 degrees of freedom (because n-1 = 19-1 = 18), the critical value is 2.100.
This critical value tells us how far away from the sample mean we can expect the population mean to be, with 95% confidence. In other words, we can be 95% confident that the population mean falls within the interval:
mean +/- (critical value * standard error)
where the standard error is simply the standard deviation divided by the square root of the sample size.
Plugging in the numbers, we get:
1.3 +/- (2.100 * (0.91 / sqrt(19)))
which equals:
1.3 +/- 0.44
Therefore, the 95% confidence interval for the mean waste recycled per person per day for the population of Tennessee is (0.86, 1.74) pounds.