Question

The owner of a restaurant that serves Continental-style entrées has the business objective of learning more about the patterns of patron demand during the Friday-to-Sunday weekend time period. She decided to study the i.) demand for dessert during this time period, ii.) the gender of the individual, and iii.) whether or not a beef entrée was ordered. Data were collected from 630 customers and organized in the following contingency tables:

Gender

Dessert Ordered	Male	Female	Total
Yes	50	96	146
No	250	234	484
Total	300	330	630

Beef Entree

Dessert Ordered	Yes	No	Total
Yes	74	68	142
No	123	365	488
Total	197	433	630

1. At the a = 0.05 level of significance, is there evidence of a difference between males and females in the proportion who order dessert?

2. At the a = 0.05 level of significance, is there evidence of a difference in the proportion who order dessert based on whether a beef entrée was ordered?

Answer 1

1. The hypothesis being tested is:

H₀: p₁ = p₂

H_a: p₁ ≠ p₂

p1	p2	pc
0.1667	0.2909	0.2317	p (as decimal)
50/300	96/330	146/630	p (as fraction)
50.	96.	146.	X
300	330	630	n
	-0.1242	difference
	0.	hypothesized difference
	0.0337	std. error
	-3.69	z
	.0002	p-value (two-tailed)

The p-value is 0.0002.

Since the p-value (0.0002) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference between males and females in the proportion who order dessert.

2. The hypothesis being tested is:

H₀: p₁ = p₂

H_a: p₁ ≠ p₂

p1	p2	pc
0.3756	0.157	0.2254	p (as decimal)
74/197	68/433	142/630	p (as fraction)
74.	68.	142.	X
197	433	630	n
	0.2186	difference
	0.	hypothesized difference
	0.0359	std. error
	6.09	z
	1.15E-09	p-value (two-tailed)

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference between males and females in the proportion who order dessert based on whether a beef entrée was ordered.