Question

A simple random sample was taken of 1000 shoppers Respondents were classified by gender (male or female) and by meat department preference (beef, chicken, fish). Results are shown in the contingency table:

Gender:	Beef	Chicken	Fish	Row Total
Male	200	150	50	400
Female	250	300	50	600
Column Total	450	450	100	1000

Is there a difference in meat preference between males and females? The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. Use a 0.05 level of significance.  

Χ² = (200 - 180)²/180 + (150 - 180)²/180 + (50 - 40)²/40
    + (250 - 270)²/270 + (300 - 270)²/270 + (50 - 60)²/60
Χ² = 400/180 + 900/180 + 100/40 + 400/270 + 900/270 + 100/60
Χ² = 2.22 + 5.00 + 2.50 + 1.48 + 3.33 + 1.67 = 16.2

As you can see, the math gets a bit cumbersome, so I did it for you!  

a & b) State the null and alternative hypotheses: Ho ___?___ , Ha ___?___

c. Which specific type of chi square test was used for this analysis? ___?___

d. What are the degrees of freedom used for this problem (columns -1)(rows -1) = df = ___?___

e. So, the P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than (enter a value) ___?___

The P-value was calculated for you: P(Χ2 > 16.2) = 0.0003

f. Based on the given information, interpret the results in symbols and values ________

g. Then interpret the results in words (full sentence) ___________

h. What will the distribution look like on a Bell curve? _____________

Answer 1

Please don't hesitate to comment for any clarification.

A)

Observed Frequencies
	Beef	Chicken	Fish	Total
Male	200	150	50	400
Female	250	300	50	600
Total	450	450	100	1000
Expected Frequencies
	Beef	Chicken	Fish	Total
Male	450 * 400 / 1000 = 180	450 * 400 / 1000 = 180	100 * 400 / 1000 = 40	400
Female	450 * 600 / 1000 = 270	450 * 600 / 1000 = 270	100 * 600 / 1000 = 60	600
Total	450	450	100	1000
	(fo-fe)²/fe
Male	(200 - 180)²/180 = 2.2222	(150 - 180)²/180 = 5	(50 - 40)²/40 = 2.5
Female	(250 - 270)²/270 = 1.4815	(300 - 270)²/270 = 3.3333	(50 - 60)²/60 = 1.6667

a) and b) Null and Alternative hypothesis:

Ho: There is no difference between the meat preference for male and female.

H1: There is a difference between the meat preference for male and female.

c) we will use chi-square test of independence.

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 16.2037

d) df = (r-1)(c-1) =(2-1)*(3-1) = 2

e) p-value = CHISQ.DIST.RT(16.2037, 2) = 0.0003

f) Decision:

p-value < 0.05, Reject the null hypothesis.

g) There is enough evidence to conclude that there is a difference between the meat preference for male and female. at 0.05 significance level.