A survey of 36 randomly selected students who dropped a course was conducted (a)
ID: 3133559 • Letter: A
Question
A survey of 36 randomly selected students who dropped a course was conducted (a) Construct a contingency table for the two variables. at a college. The following results were collected. Work Course Persona. Full data set Male M Work M Work M Work Female F Work F Personal M Personal F Work IMI Work: MI Personal M Personal F Course F Course b) Test whether gender is independent of drop reason at the a 0.1 level of M Work FT Personal IMI Work significance M Personal F Personal M Course What are the hypotheses? Work Md M Course F Course M Personal F Personal M Personal Ho: p F Personal FI Course DMI Work H1: At least one of the proportions is different from the others. M Work M Course DM Personal F Work M Work F Personal OB. Ho: Oc EC and O Ep and O Ew M Personal Course EM Work H1: Oc Ec or OP EP or ow Ew C. Ho: Gender and drop reason are independent. HI: Gender and drop reason are dependent Determine the P-value P-value (Round to three decimal places as needed.)Explanation / Answer
a)
Doing an Expected Value Chart,
5.111111111 8.944444444 8.944444444
2.888888889 5.055555556 5.055555556
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 0.627806976 [ANSWER, TEST STATISTIC]
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With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 3
b = 2
df = 2
Thus, the critical value is
significance level = 0.1
chi^2(critical) = 4.605170186
Also, the p value is
P = 0.730589536 [ANSWER, P VALUE]
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As P > 0.10, we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that gender is dependent of drop reason. [CONCLUSION]
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