Students in an Introductory Statistics class at a large university were classified by birth order and by the college they attend.

a) What kind of chi-square test is appropriate€”goodness-of-fit, homogeneity, or independence?
b) State your hypotheses.
c) State and check the conditions.
d) How many degrees of freedom are there?
e) The calculation yields x2 = 17.78, with P = 0.0378. State your conclusion.
f) Examine and comment on the standardized residuals.
Do they challenge your conclusion? Explain.

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Birth Order (1 oldest or only child) Arts and Sciences 34 46 Agriculture Social Science Professional Total 52 27 5 15 17 8 13 111 114 69 20 1 2 3 4 or More Total 57 93 43 31 224 21 Expected Values Birth Order (1-oldest or only child) 4 or More Arts and Snces 29.0089 17.5580 5.0893 5.3438 473304 28.6473 8.3036 8.7188 21.8839 13.2455 3.8393 4.0313 15.7768 9549 2.7679 2.9063 g Agriculture Social Science Professional