Q2) Chi-Square Test for Goodness of Fit (9 points total) A high school teacher w

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Q2) Chi-Square Test for Goodness of Fit (9 points total) A high school teacher wondered if the college-bound graduates this year would be evenly split in terms of their majors. She collected the information from a random sample of 100 graduates as follows: Social sciences- 35, natural sciences- 20, fine arts- 15, liberal arts- 30. Conduct a Chi-square test for goodness of fit with an alpha level of .01 to answer her question.

a) What is the variable being examined in this study? (1 point)

b) State the null and alternative hypotheses in words (1 point each, 2 points total)

c) Calculate X2 statistic (1 for formula/work, 1 for result, 2 points total)

d) Identify the critical value (1 point)

e) Compare the X2 statistic with the critical value (1 point)

f) Report the hypothesis test result, using “reject” or “fail to reject” in the answer (1 point)

g) Explain the conclusion in a sentence or two (1 point)

Explanation / Answer

a) What is the variable being examined in this study?

Answer : The variable here being examined is the number of college bound graduates in each stream.

b) State the null and alternative hypotheses in words ?

Null Hypothesis : Ho : There is no difference between number of college bound graduate students in each stream.

Alternative Hypothesis : Ha : there is significant difference between number of college bound graduate students in each stream.

c) Calculate X2 statistic

X2   = (35-25)2/25 + (20 - 25)2 /25 + (15-25)2 /25 + ( 30-25)2 /25 = 4+1+4+1 =10

d) Identify the critical value (1 point)

X2 criical for dF = 3 and alpha = 0.01 =>X2 criical = 11.345

e) Compare the X2 statistic with the critical value .

Here X2 < X2critical so we cannot reject the null hypothesis.

f) Report the hypothesis test result, using “reject” or “fail to reject” in the answer (1 point)

We cannot reject the null hypothesis.

g) Explain the conclusion in a sentence or two (1 point)

We can conclude that there is no significance difference between college bound graduates across various streams.

Stream Observed Number Expected Social Sciences 35 25 natural Sciences 20 25 Fine arets 15 25 Liberal arts 30 25

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