Question

Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place are shown below.

Frequencies of Breakfasts for Men and Women

	French Toast	Pancakes	Waffles	Omelets
Men	93	51	86	71
Women	66	67	100	50

What can be concluded at the α = 0.01 significance level?

1. What is the correct statistical test to use?
   • Goodness-of-Fit
   • Paired t-test
   • Homogeneity
   • Independence
2. What are the null and alternative hypotheses?
   H0:
   • Breakfast ordered and gender are independent.
   • The distribution of breakfast ordered for men is the same as it is for women.
   • The distribution of breakfast ordered for men is not the same as it is for women.
   • Breakfast ordered and gender are dependent.
   
   H1:
   • Breakfast ordered and gender are independent.
   • The distribution of breakfast ordered for men is the same as it is for women.
   • The distribution of breakfast ordered for men is not the same as it is for women.
   • Breakfast ordered and gender are dependent.
3. The test-statistic for this data = ______ (Please show your answer to three decimal places.)  
   
4. The p-value for this sample = _____ (Please show your answer to four decimal places.)  
   
5. The p-value is? (greater than, less than or equal to) α  
   
6. Based on this, we should
   • reject the null
   • accept the null
   • fail to reject the null
7. Thus, the final conclusion is...
   • There is sufficient evidence to conclude that breakfast ordered and gender are dependent.
   • There is insufficient evidence to conclude that the distribution of breakfast ordered for men is not the same as it is for women.
   • There is sufficient evidence to conclude that the distribution of breakfast ordered for men is not the same as it is for women
   • There is insufficient evidence to conclude that breakfast ordered and gender are dependent.
   • There is sufficient evidence to conclude that the distribution of breakfast ordered for men is the same as it is for women.

Answer 1

Homogeneity

Ho: The distribution of breakfast ordered for men is the same as it is for women.

Ha: The distribution of breakfast ordered for men is not the same as it is for women.

Applying chi square test of homogeneity

Expected	Ei=row total*column total/grand total	French toast	Pancakes	Waffles	Omletes	Total
	Men	81.9503	60.8185	95.8664	62.3647	301
	Women	77.0497	57.1815	90.1336	58.6353	283
	total	159	118	186	121	584
chi square    χ2	=(Oi-Ei)2/Ei	French toast	Pancakes	Waffles	Omletes	Total
	Men	1.490	1.585	1.015	1.196	5.2861
	Women	1.585	1.686	1.080	1.272	5.6223
	total	3.0745	3.2710	2.0955	2.4674	10.9084
test statistic X2=		10.908
p value =	0.0122	from excel: chidist(10.9084,3)

fail to reject the null

There is insufficient evidence to conclude that the distribution of breakfast ordered for men is not the same as it is for women.