Question

Twenty-five wooden beams were ordered or a construction project. The sample mean and he sample standard deviation were measured xbar = 190cm, s = 5cm. Calculated confidence interval for the mean is [188.29; 191.71].

Which confidence level was chosen? Assume distribution to be normal.
A. 99%
B. 90%
C. 95%
D. 99.9%

Answer 1

Correct option: B. 90%

Step-by-step explanation:

The confidence interval is given by:

`CI = [\bar{x} - z\sigma_{\bar{x}} , \bar{x}+z\sigma_{\bar{x}} ]`

If
`\bar{x}` is 190, we can find the value of
`z\sigma_{\bar{x}}`:

`\bar{x} - z\sigma_{\bar{x}} = 188.29`

`190 - z\sigma_{\bar{x}} = 188.29`

`z\sigma_{\bar{x}} = 1.71`

Now we need to find the value of
`\sigma_{\bar{x}}`:

`\sigma_{\bar{x}} = s / √(n)`

`\sigma_{\bar{x}} = 5/ √(25)`

`\sigma_{\bar{x}} = 1`

So the value of z is 1.71.

Looking at the z-table, the z value that gives a z-score of 1.71 is 0.0436

This value will occur in both sides of the normal curve, so the confidence level is:

`CI = 1 - 2*0.0436 = 0.9128 = 91.28\%`

The nearest CI in the options is 90%, so the correct option is B.