A professor is trying to determine if her students guessed on a certain multiple choice question. She expects that if the students guessed, the distribution of answers would be uniform for that question. She compares the observed distribution of answers with the uniform distribution. The professor conducts a chi-square Goodness-of-Fit hypothesis test at the 1% significance level. Answer Choice A B C D Expected 15 15 15 15 Observed 19 20 14 7 (a) The null and alternative hypotheses are: H0: The student answers have the uniform distribution. Ha: The student answers do not have the uniform distribution. (b) Compute the test statistic, rounded to three decimal places

The chi-square test statistic is given by the sum of the divisions between the squared difference of each observation and the expected value, by the expected value.

The squared differences in this problem are given as follows:

(19 - 15)². -> Choice A.

(20 - 15)² -> Choice B.

(14 - 15)² -> Choice C.

(7 - 15)² -> Choice D.

All these measures are taken from the table presented in this problem. The expected value is of 15 because there is a total of 60 observations and 4 possible results, hence 60/4 = 15.

Hence the test statistic is calculated as follows:

χ² = (19 - 15)²/15 + (20 - 15)²/15 + (14 - 15)²/15 + (7 - 15)²/(19 - 15)²

χ² = 6.8.

More can be learned about the chi-square test statistic at https://brainly.com/question/4543358

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