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	82	51	92	70
Women	98	60	112	53

What can be concluded at the αα = 0.05 significance level?

1. What is the correct statistical test to use?
   • Paired t-test
   • Goodness-of-Fit
   • Homogeneity
   • Independence
2. What are the null and alternative hypotheses?
   H0:H0:
   • Breakfast ordered and gender are independent.
   • Breakfast ordered and gender are dependent.
   • The distribution of breakfast ordered for men is not the same as it is for women.
   • The distribution of breakfast ordered for men is the same as it is for women.
   
   
   
   
   
   
   
   H1:H1:
   • Breakfast ordered and gender are dependent.
   • The distribution of breakfast ordered for men is the same as it is for women.
   • Breakfast ordered and gender are independent.
   • The distribution of breakfast ordered for men is not the same as it is for women.
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 Select an answer greater than less than (or equal to)  αα  
   
   
   
   
   
6. Based on this, we should
   • accept the null
   • fail to reject the null
   • reject the null
7. Thus, the final conclusion is...
   • There is sufficient evidence to conclude that the distribution of breakfast ordered for men is the same as it is for women.
   • There is sufficient evidence to conclude that breakfast ordered and gender are dependent.
   • There is insufficient 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

Answer 1

Men Women Total French toast 82 98 180 Pancakes 51 60 111 Waffles 92 112 204 Omelets 70 53 123 Total 295 323 618 Expected values French toast 85.9223 Pancakes 52.9854 Men Women Waffles 97.3786 106.6214 Omelets 58.7136 64.2864 94.0777 58.0146

Chi - square distribution table. Observed (0) Expected (E) Chi square =(O-E)/E 82 85.9223 51 92 70 98 60 112 52.9854 97.3786 58.7136 94.0777 58.0146 106.6214 64.2864 0.1791 0.0744 0.2971 2.1696 0.1635 0.0679 0.2713 1.9815 5.2044 53 Total Test statistic y? = E(C-5) = 5.2044 Df=(c-1)(r-1)=(2-1)(4-1)=3 p-value=CHIDIST(5.204,3)= 0.1575 Since p-value > 0.05 hence fail to reject the null hypothesis

Answers are Chi-square test for independence Null hypothesis is Ho: Breakfast ordered and gender are independent Alternate hypothesis is Hz: Breakfast ordered and gender are dependent Test statistic Test statistic y2 = 3( =***)= 5.204 P-value = 0.1575 Since p-value >a Based on this we should fail to reject H, Final conclusion There is insufficient evidence to conclude that the distribution of breakfast ordered for men are dependent]