Question

A research company desires to know the mean consumption of meat per week among people over age 23. A sample of 164 people over age 23 was drawn and the mean meat consumption was 4.1 pounds. Assume that the population standard deviation is known to be 0.7 pounds. Construct the 80% confidence interval for the mean consumption of meat among people over age 23. Round your answers to one decimal place.

Answer 1

The 80% confidence interval for the mean consumption of meat among people over age 23 is between 4 and 4.2 pounds.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.8)/(2) = 0.1`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.1 = 0.9`, so
`z = 1.28`

Now, find M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

`M = 1.28*(0.7)/(√(164)) = 0.07`

The lower end of the interval is the mean subtracted by M. So it is 4.1 - 0.07 = 4.03 pounds

The upper end of the interval is the mean added to M. So it is 4.1 + 0.07 = 4.17 pounds

Rounded to one decimal place

The 80% confidence interval for the mean consumption of meat among people over age 23 is between 4 and 4.2 pounds.