Question

You measure the weights of a random sample of 400 male workers in the automotive industry. The sample mean is = 176.2 lbs. Suppose that the weights of male workers in the automotive industry follow a normal distribution with unknown mean μ and standard deviation σ = 11.1 lbs. A 95% confidence interval for μ is:

Answer 1

A 95% confidence interval for μ is (175.287 lbs, 177.113 lbs).

Explanation:

By the Central Limit Theorem, the mean of the sample is the same as the mean of the population. So:

Building the confidence interval:

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

`\alpha = (1-0.9)/(2) = 0.05`

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
`1-0.05 = 0.95`, so
`z = 1.645`

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 = 1.645*(11.1)/(√(400))= 0.9130`

The lower end of the interval is the mean subtracted by M. So it is 176.2 - 0.9130 = 175.287 lbs

The upper end of the interval is the mean added to M. So it is 176.2 + 0.9130 = 177.113 lbs.

A 95% confidence interval for μ is (175.287 lbs, 177.113 lbs).