Final answer:
In this case, the test statistic is 1.69, which is greater than the critical value, so we conclude that the variance of the old machine is significantly larger than that of the new one.
Therefore, the correct answer is: option c). The test statistic is approximately 1.69.
Step-by-step explanation:
To test if the variance of the old machine is significantly larger than that of the new one, we can use a hypothesis test.
The null hypothesis (H0) is that the variance of the old machine is not significantly larger, and the alternative hypothesis (HA) is that the variance of the old machine is significantly larger.
To conduct the test, we can use the F-test for comparing variances. The test statistic is the ratio of the sample variances: F = s2(old) / s2(new)
With a significance level of 5%, and degrees of freedom of (n1-1) = 43 and (n2-1) = 44, the critical value for the F-test is approximately 2.41.
If the test statistic F is greater than the critical value, then we reject the null hypothesis and conclude that the variance of the old machine is significantly larger.
In this case, we do not have the values of the sample variances, only the standard deviations.
To calculate the test statistic, we need to square the standard deviations: F = (s(old))^2 / (s(new))^2 = 11^2 / 9^2.
Evaluating this expression gives us the test statistic F = 1.69, which is greater than the critical value of 2.41.
Therefore, we reject the null hypothesis and conclude that the variance of the old machine is significantly larger than that of the new one.