Question

a. State the Null and Alternative Hypotheses in words.

b. Perform the appropriate hypothesis test using an Alpha of .05. Be sure to write what critical value you are using in your work.

c. State your results first by saying whether you reject or fail to reject the null hypothesis. Then state the conclusion in your own words.

d. type in your hypotheses, the df value you use, and the critical value. Also include your conclusion and When you calculate Chi-Square, write out your work.

Question: A restaurant manager wants to know if one of the three specials on the menu (baked fish, roasted beef, or chicken salad) is more popular than the others. She selects a random sample of special orders and counts the number of orders in each category. The results are compiled in the following table. Fish: 52, Beef 42, Chicken 29

Answer 1

Question: A restaurant manager wants to know if one of the three specials on the menu (baked fish, roasted beef, or chicken salad) is more popular than the others. She selects a random sample of special orders and counts the number of orders in each category.

Chi-square test of independence

Solution:

Here, we have to use chi square test for independence of two categorical variables.

a. State the Null and Alternative Hypotheses in words.

Null hypothesis: H₀: No one of the three specials on the menu (baked fish, roasted beef, or chicken salad) is more popular than the others.

Alternative hypothesis: H_a: One of the three specials on the menu (baked fish, roasted beef, or chicken salad) is more popular than the others.

b. Perform the appropriate hypothesis test using an Alpha of .05. Be sure to write what critical value you are using in your work.

We are given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

Degrees of freedom = df = n – 1 = 3 – 1 = 2

α = 0.05

Critical value = 5.991464547

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

	O	E	(O - E)	(O - E)^2	(O - E)^2/E
Fish	52	41	11	121	2.951219512
Beef	42	41	1	1	0.024390244
Chicken	29	41	-12	144	3.512195122
Total	123	123			6.487804878

Chi square = ∑[(O – E)^2/E] = 6.487804878

P-value = 0.039011358

(By using Chi square table or excel)

c. State your results first by saying whether you reject or fail to reject the null hypothesis. Then state the conclusion in your own words.

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that one of the three specials on the menu (baked fish, roasted beef, or chicken salad) is more popular than the others.

Part d

We reject the claim (Chi square = 6.49, df = 2, P = 0.039) that one of the three specials on the menu (baked fish, roasted beef, or chicken salad) is more popular than the others.