Errors and Power Practice

Question

Question 5 (1 point)

At a manufacturing company for medical supplies, machines produce parts used in highly specialized lasers. Company researchers are testing a new machine designed to improve the precision of the parts. The null hypothesis is that the new machine does not improve the precision. For the researchers, the more consequential error would be that the new machine actually improves the precision, but the test does not detect the improvement.

a	Decrease the significance level to increase the probability of a Type I error.
b	Decrease the significance level to decrease the standard error.
c	Increase the significance level to decrease the probability of a Type I error.
d	Decrease the significance level to decrease the probability of a Type I error.
e	Increase the significance level to increase the probability of a Type I error.

Question 6 (1 point)

A university will add fruit juice vending machines to its classroom buildings if the student body president is convinced that more than 20 percent of the students will use them. A random sample of n students will be selected and asked whether or not they would use the vending machines. A large-sample test for proportions at the significance level of α = 0.05 will be performed. The null hypothesis that the proportion of all students who would use the vending machines is 20 percent will be tested against the alternative that more than 20 percent of all students would use them. For which of the following situations would the power of the test be highest?

a	The sample size is n = 1,000, and 50 percent of all students use the vending machines.
b	The sample size is n = 750, and 20 percent of all students use the vending machines.
c	The sample size is n = 1,000, and 25 percent of all students use the vending machines.
d	The sample size is n = 750, and 25 percent of all students use the vending machines.
e	The sample size is n = 500, and 50 percent of all students use the vending machines.

Answer 1

You are less likely to make a Type I error if you increase the significance level (c)

The larger the sample size and the further the sample proportion from the hypothesized proportion in the direction being tested by the alternate hypothesis, the greater the power, so (a).