The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week generated in the city. The study included 128 residents whose mean number of pounds of trash generated per person per week was 36.3 pounds, with a standard deviation of 6.7 pounds. Round answers to 3 decimal places where possible.

a. To compute the confidence interval, use a [t or z] distribution.
b. With 95% confidence, the population mean number of pounds per person per week is between ? and ? pounds.
c. If many groups of 128 randomly selected members are studied, then a different confidence interval would be produced from each group. About ? percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week, and about ? percent will not contain the true population mean number of pounds of trash generated per person per week.

In this problem, we use a t-distribution to calculate the 95% confidence interval for the amount of trash generated per person per week. The interval is between 35.125 and 37.475 pounds. Around 95% of all confidence intervals from possible samples will contain the population mean, while about 5% will not.

Explanation:

For this problem, we should use a t-distribution because we don't know the standard deviation of the population. Since we are only given a sample standard deviation, t-distribution is most appropriate.

Now, let's calculate the confidence interval. The formula for a t-confidence interval is: x ± t * (s/√n). We have all these values; x (sample mean) = 36.3, t = t-critical for 95% confidence with 127 degrees of freedom (1.98 from the t-distribution table), s (sample standard deviation) = 6.7, and n (sample size) = 128.

The standard error 's/√n' equals about 0.593. Therefore, the confidence interval is 36.3 ± 1.98 * 0.593. That comes to between 35.125 and 37.475 pounds.

About 95% of the confidence intervals of all possible samples of size 128 will contain the true population mean number of pounds of trash generated per person per week. Therefore, about 5% will not contain the true population mean.

Learn more about t-distribution here:

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