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The mayor is interested in finding a 90% confidence interval for the mean number of pounds of trash per person per week generated in the city. The study included 156 residents, whose mean number of pounds of trash generated per person per week was 36.7 pounds, with a standard deviation of 7.9 pounds. Round answers to 3 decimal places where possible.

a. To compute the confidence interval, use a t-distribution.

b. With 90% confidence, the population mean number of pounds per person per week is between _____ and _____ pounds.

Answer :

a. To compute the 90% confidence interval for the mean number of pounds of trash per person per week generated in the city, we can use the t-distribution.

b. With 90% confidence, the population mean number of pounds per person per week is between 35.535 pounds and 37.865 pounds.

a. To compute the confidence interval, we'll use the formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

Since the sample size is large (n > 30), we can approximate the critical value using the standard normal distribution. For a 90% confidence level, the critical value is approximately 1.645.

Plugging in the values, the confidence interval is:

36.7 ± 1.645 * (7.9 / sqrt(156)) = 36.7 ± 1.645 * 0.633 = 36.7 ± 1.041

Rounding to three decimal places, the confidence interval is (35.659, 37.741).

b. With 90% confidence, we can state that the population mean number of pounds per person per week is between 35.535 pounds and 37.865 pounds.

Learn more about confidence intervals here: brainly.com/question/32546207

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