(D) They should conclude that there is no evidence of an association between grade level and
opinion on the theme because the test statistic is higher than the critical value for 3 degrees of
freedom.
(E) They should conclude that there is no evidence of an association between grade level and
opinion on the theme because the test statistic is lower than the critical value for 3 degrees of
freedom.
A quality control manager of a company that produces, among other things, parts for games wants to
be sure the dice produced by the company are fair. An employee is told to take a single die, roll it
10,000 times, and record the number of times each face appears. Instead, he rolls it 100 times and
multiplies the result by 100. Which of the following describes a likely effect of this approach on the
chi-square test results?
(A) Because the chi-square test is based on each face appearing one-sixth of the time, the number of
trials should not affect the chi-square statistic. This approach is valid.
(B) Multiplying the frequencies by 100 will multiply the chi-square statistic by 100, making the test
much more powerful. As a result, an unfair die is more likely to be detected.
(C) With the lower number of trials, we expect greater variation in proportions, so the chi-square
statistic will probably be too large, resulting in a greater chance of a fair die being labeled
unfair.
(D) With the lower number of trials, we expect smaller differences between observed and expected
frequencies, so the chi-square statistic will probably be too small, resulting in a greater chance
of an unfair die being labeled fair.
(E) With the lower number of trials, there is more bias in the results, so there is a greater chance of
a fair die being labeled unfair.