Final answer:
To test if men and women differ in repeatability of assembling components on circuit boards, an F-test for variances can be conducted comparing the two sample standard deviations at a 5 percent level of significance.
Step-by-step explanation:
To determine if there is evidence to support the claim that men and women differ in repeatability for assembling components on printed circuit boards, we can use the F-test for variances. This is appropriate since the question involves comparing two sample standard deviations to see if they are significantly different from each other. The null hypothesis (H0) for this test states that the variances are equal, while the alternative hypothesis (H1) states that the variances are not equal.
The formula for the F-test is:
F = variance of the first group / variance of the second group
In this case, the variances are the squares of the given standard deviations:
- Variance of men, S2men = (0.9)2
- Variance of women, S2women = (1.02)2
The F-test statistic is calculated as:
F = (0.9)2 / (1.02)2
The degrees of freedom for the numerator (men) is 24 (n-1 = 25-1) and for the denominator (women) is 20 (n-1 = 21-1). Using the F-distribution table or a calculator, we compare the calculated F-test statistic with the critical F-value at the 5 percent level of significance for 24 and 20 degrees of freedom. If the calculated F-value is greater than the critical F-value, we reject the null hypothesis, indicating that there is a significant difference in variances, hence in repeatability.
If the null hypothesis is not rejected, it suggests there is not enough evidence to conclude a difference in repeatability between men and women for this task. It's important to note that if the null hypothesis is rejected, it does not necessarily mean that one gender is better or worse at the task, just that their repeatability differs.