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.

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