Question

Do blondes have more fun? Walking around downtown saturday night, you ask people whether they had a boring time, a good time, or a great time that night, and note their hair color. Out of 80 blondes: 20 had a boring night, 20 had a good night, and 40 had a great night. out of 120 non-blondes: 30 had a boring night, 40 had a good night, and 50 had a great night. What is the chi-square value for this data (type in box 1 to two decimal places) and is there statistically significant relationship between hair color and fun at the .05 level (type yes or no in box 2)?

Answer 1

Null Hypothesis H0: There is no relationship between Hair color and fun

Alternative Hypothesis H1: The Hair color and fun are related to each other

The contingency table is

	Boring night	Good night	Great night	Total
Blonde	20	20	40	80
Non Blone	30	40	50	120
Total	50	60	90	200

Significance Level

Degrees of freedom = (r-1)*(c-1) = (2-1)*(3-1) = 2

Under H0, the expected frequencies are

	Obs. Freq( O)				Exp. Freq( E )
	Boring night	Good night	Great night	Total	Boring night	Good night	Great night	Total
Blonde	20	20	40	80	20	24	36	80
Non Blone	30	40	50	120	30	36	54	120
Total	50	60	90	200	50	60	90	200
Calculations for Chi Square Test:
	Obs. Freq( O )	Exp.Freq. ( E )	(O-E)^2/E
	20	20	0.000
	20	24	0.667
	40	36	0.444
	30	30	0.000
	40	36	0.444
	50	54	0.296
Total	200	200	1.852

The Chi square test statistic is

The critical value of chi square for 2 df at 5% significance level is 5.991

Since chi square calculated is less than chi square tabulated. Fail to Reject H0.

Hence at 5% significance level, we have enough evidence to conclude that there is no  statistically significant relationship between hair color and fun.

Answer:

No