Question

A fast food restaurant executive wishes to know how many fast food meals teenagers eat each week. They want to construct a 85% confidence interval for the mean and are assuming that the population standard deviation for the number of fast food meals consumed each week is 1.4 . The study found that for a sample of 502 teenagers the mean number of fast food meals consumed per week is 3.1 . Construct the desired confidence interval. Round your answers to one decimal place. Lower end point and Upper end point

Answer 1

The 85% confidence interval for the mean number of fast food meals each week is (3.01 meals, 3.19 meals).

Explanation:

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

`\alpha = (1-0.85)/(2) = 0.075`

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
`1-0.075 = 0.925`, so
`z = 1.44`

Now, find M as such

`M = z*(\sigma)/(√(n))`

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

`M = 1.44*(1.4)/(√(502)) = 0.09`

The lower end of the interval is the mean subtracted by M. So it is 3.1 - 0.09 = 3.01 meals.

The upper end of the interval is the mean added to M. So it is 3.1 + 0.09 = 3.19 meals.

The 85% confidence interval for the mean number of fast food meals each week is (3.01 meals, 3.19 meals).