A proofreader checked 160 ads for grammatical errors.The distribution obtained is shown below. At α = .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 below.  At α = .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 determine whether the sample came from a uniform distribution, we can use a goodness-of-fit test. The expected frequencies for a uniform distribution with 160 observations and 5 categories (0-31, 32-63, 64-95, 96-127, 128-159) would be 32 for each category. We can calculate the expected frequencies for each category and compare them to the observed frequencies using a chi-square test. If the calculated chi-square value is greater than the critical value at α = .01 with 4 degrees of freedom, we can reject the null hypothesis of a uniform distribution. In this case, the calculated chi-square value is 35.6, which is greater than the critical value of 13.28. Therefore, we reject the null hypothesis and conclude that the distribution is not uniform.

A Proofreader Checked 160 Ads for Grammatical Errors