Question

(25 pts) A coffee enthusiast would like to test whether the coffee preference of young consumers living in Brooklyn is affected by the perceived brand. He recruits 18 volunteers and divides them into 3 groups: one group gets coffee in a starbucks cup, another group gets coffee in a McDonalds cup, and a third group gets coffee in a cup labeled “new Fair-Trade Organic no GMO Rainforest” coffee. The catch is that everyone receives the same brewed coffee. The participants are asked to drink as much coffee as they can tolerate out of an 8oz serving. Below is the number of ounces consumed by each of the 18 people. Test the hypothesis that perceived brand affects preference for coffee (use alpha = .05).

McDonalds	Starbucks	NFTONGMOR
1	2	8
0	1	8
2	2	7
1	3	8
1	1	8
2	4	8

1. (2 pts) Find the critical value:
2. (4 pts) Calculate the obtained statistic (DO THIS BY HAND HERE):
3. (2 pts) Make a decision
4. (2 pts) What does your decision mean?
5. (3 pts) Perform this test in SPSS and paste the proper output here:
6. (3 pts) Explain in words which part of the output specifically indicates which decision to make about the null hypothesis.
7. (4 pts) Is a post-hoc test appropriate here? Why or why not? If it is, run the post-hoc and explain the results:

Answer 1

The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: At least one means is not equal

The calculations are:

	Mean	n	Std. Dev
	1.2	6	0.75	McDonalds
	2.2	6	1.17	Starbucks
	7.8	6	0.41	NFTONGMOR
	3.7	18	3.12	Total
				F crit 3.68232
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	155.11	2	77.556	110.79	1.04E-09
Error	10.50	15	0.700
Total	165.61	17

(2 pts) Find the critical value:

The critical value is 3.68232.

(4 pts) Calculate the obtained statistic (DO THIS BY HAND HERE):

The obtained statistic is 110.79.

Make a decision

Since 110.79 > 3.68232, we can reject the null hypothesis.

What does your decision mean?

Therefore, we can conclude that the perceived brand affects preference for coffee.

pts) Perform this test in SPSS and paste the proper output here:

The SPSS output is:

Explain in words which part of the output specifically indicates which decision to make about the null hypothesis.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Is a post-hoc test appropriate here? Why or why not? If it is, run the post-hoc and explain the results:

Since the perceived brand affects preference for coffee, we need to do the post-hoc test here.

The post-hoc results are:

Post hoc analysis
p-values for pairwise t-tests
		McDonalds	Starbucks	NFTONGMOR
		1.2	2.2	7.8
McDonalds	1.2
Starbucks	2.2	.0561
NFTONGMOR	7.8	6.25E-10	5.89E-09
Tukey simultaneous comparison t-values (d.f. = 15)
		McDonalds	Starbucks	NFTONGMOR
		1.2	2.2	7.8
McDonalds	1.2
Starbucks	2.2	2.07
NFTONGMOR	7.8	13.80	11.73

There is a significant difference between NFTONGMOR and McDonalds.

There is a significant difference between NFTONGMOR and Starbucks.