A proofreader checked 160 ads for grammatical errors. The distribution obtained is shown: $$\begin{array} { | l | c | c | c | c | }
\hline \text { Number of Errors } & 0 & 1 & 2 & 3 \
\hline \text { Observed Frequency } & 10 & 65 & 71 & 14 \
\hline
\end{array}$$ At ? = .01, what decision would we reach in a goodness-of-fit test to see whether this sample came from a uniform distribution?
A)Reject the null and conclude the distribution is not uniform.
B)Conclude that there is insufficient evidence to reject the null.
C)No conclusion can be made due to small expected frequencies.
D)No conclusion can be made due to inadequate sample size.

Question

A proofreader checked 160 ads for grammatical errors. The distribution obtained is shown: $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Number of Errors } & 0 & 1 & 2 & 3 \
\hline \text { Observed Frequency } & 10 & 65 & 71 & 14 \
\hline
\end{array}$$ At ? = .01, what decision would we reach in a goodness-of-fit test to see whether this sample came from a uniform distribution?
A)Reject the null and conclude the distribution is not uniform.
B)Conclude that there is insufficient evidence to reject the null.
C)No conclusion can be made due to small expected frequencies.
D)No conclusion can be made due to inadequate sample size.

Quizplus · Accepted Answer

To test whether the sample follows a uniform distribution, we need to calculate the expected frequency for each category. Since there are four categories and a total of 160 ads (sample size), the expected frequency for each category is 40 (i.e., 160/4). The null hypothesis is that the observed frequencies follow a uniform distribution, and the alternative is that they do not. We can use a chi-square test to calculate the test statistic, which is 40.25. The degrees of freedom are 3 because there are 4-1=3 independent categories. At α = .01 and df=3, the critical value of chi-square is 11.345. Since the test statistic is greater than the critical value, we reject the null and conclude that the distribution is not uniform. Therefore, the answer is A.

A Proofreader Checked 160 Ads for Grammatical Errors At ? = 01, What Decision Would We Reach in a Goodness-Of-Fit Test