Question

a research company desires to know the mean consumption of meat per week among people over age 32. a sample of 576 people over age 32 was drawn and the mean meat consumption was 4.9 pounds. assume that the population standard deviation is known to be 1 pounds. construct the 85% confidence interval for the mean consumption of meat among people over age 32. round your answers to one decimal place.

Answer 1

The 85% confidence interval for the mean consumption of meat among people over age 32 is 4.8 to 5.0 pounds.

Explanation:

To construct a confidence interval for the mean consumption of meat among people over age 32, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

Given that the sample size is 576, the sample mean is 4.9 pounds, and the population standard deviation is 1 pound, we can calculate the standard error using the formula:

Standard Error = Population Standard Deviation / √Sample Size

Standard Error = 1 / √576 ≈ 0.0412

The critical value is based on the desired confidence level. In this case, we want an 85% confidence interval.

Since the confidence interval is two-tailed, we need to find the critical value that leaves 7.5% in each tail of the distribution.

Using a standard normal distribution table or a calculator, we find the critical value to be approximately 1.4398.

Now we can calculate the confidence interval:

Confidence Interval = 4.9 ± (1.4398 * 0.0412)

Confidence Interval = 4.9 ± 0.0594

Confidence Interval = (4.8406, 4.9594)

Therefore,

The 85% confidence interval for the mean consumption of meat among people over age 32 is 4.8 to 5.0 pounds.