The correct significance level for this test, where we reject the null hypothesis, would be:
D. Level of significance = 99%
How to determine the significance level for this test
To determine the significance level for this test, compare the observed mean diameter to the target diameter and assess whether it has moved away significantly.
In hypothesis testing, set up null and alternative hypotheses.
In this case, the null hypothesis (H0) would be that the mean diameter of the spindle is 40 mm, and the alternative hypothesis (Ha) would be that it is different from 40 mm.
Since the manufacturer wants to determine if the mean diameter has moved away from the target (40 mm), use a two-tailed test. This means we need to consider deviations in both directions.
To determine the significance level, compare the observed mean diameter (40.3 mm) to the target diameter (40 mm) and consider the standard deviation (0.5 mm). Calculate the test statistic, which is the number of standard deviations away from the mean the observed value is.
Test statistic (z-score) = (observed mean - target mean) / (standard deviation /
(sample size))
z = (40.3 - 40) / (0.5 /
(100))
z = 0.3 / (0.5 / 10)
z = 0.3 / 0.05
z = 6
Now, for a two-tailed Z-test at a 95% confidence level, the critical Z-value is approximately ±1.96.
Since the calculated Z-score of 6 is much larger than the critical Z-value of ±1.96, we can reject the null hypothesis and conclude that there is a significant difference in the mean diameter from the target.
The correct significance level for this test, where we reject the null hypothesis, would be:
D. Level of significance = 99%