40 randomly selected items were tested. It was found that the average of the sample was 469.
The standard deviation of the items tested is 73.
Test the hypothesis that the mean is exactly 475 at α = 0.10
State the null and alternative hypothesis:
H0: μ = 475HA: μ ≠ 475
Calculate our test statistic z:
| z = | X - μ |
| σ/√n |
| z = | 469 - 475 |
| 73/√40 |
| z = | -6 |
| 73/6.3245553203368 |
| z = | -6 |
| 11.542313459615 |
z = -0.51982646468521
Determine rejection region:
Since our null hypothesis is H0: μ = 475, this is a two tailed testChecking our table of z-scores for α(left); = 0.05 and α(right); = 0.95, we get:
Z left tail of = -1.6449 and Z right tail of 1.6449
Our rejection region is Z < -1.6449 and Z > 1.6449
Since our test statistic of -0.51982646468521 is not in the rejection region, we accept (cannot reject) H0
