Question

1. Arty Artlover was studying art appreciation. He selected an abstract painting that had no obvious top or bottom. Subjects were asked to hang the painting whichever way they thought it should be correctly hung. The following table shows how many of the 50 subjects reported each direction. Test at an α = .05 to determine if there were significant differences in the reported direction the painting was hung. Note: assume all directions were equally likely. (8 points)

Top Up (Correct)	Bottom Up	Left Side Up	Right Side Up
18	17	7	8

Answer 1

null hypothesis: Ho: all directions were equally likely

Alternate hypothesis: Not all directions were equally likely

degree of freedom =categories-1=			3
for 0.05 level and 3 degree of freedom :rejection region =					7.815
applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
top up	0.250	18.000	12.500	1.56	2.420
bottom up	0.250	17.000	12.500	1.27	1.620
left side up	0.250	7.000	12.500	-1.56	2.420
right side up	0.250	8.000	12.500	-1.27	1.620
total	1.000	50	50		8.080

test statistic X² =8.080

as test statistic falls in rejection region , we reject null hypothesis.

we have sufficient evidence at 0.05 level to conclude that Not all directions were equally likely