Question

Question Part Points Submissions Used Problem 10-9 A sample of 80 observations is taken from a population of unknown mean wherein the standard deviation is assumed to be 5 grams. The computed value of the sample mean is 32.7 grams. Construct confidence intervals for each of the following levels of confidence:90% confidence interval : ______

Answer 1

The 90% confidence interval is (31.78 grams, 33.62 grams).

Explanation:

The first step is finding 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`, that is between
`Z = 1.64` and
`Z = 1.65`, so we use
`z = 1.645`.

Now, find M as such:

`M = z*(\sigma)/(√(n)) = 1.645*(5)/(√(80)) = 0.92`

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

The lower end of the interval is the sample mean subtracted by M. So it is 32.7 - 0.92 = 31.78 grams.

The upper end of the interval is the sample mean added to M. So it is 32.7 + 0.92 = 33.62 grams.

The 90% confidence interval is (31.78 grams, 33.62 grams).