Question

Question 1: You are evaluating whether the use of red lights during evaluation has a significant effect on liking. Liking was measured as either like or dislike. You collected the below data. Using the Sign Test, did the wine glass significantly influence liking? There is a worked example using the sign test   (5 pts)

Panelist	Liking of wine: No red light	Liking of wine: With Red light	Direction of change
1	Like	Like
2	Dislike	Like
3	Dislike	Like
4	Dislike	Like
5	Like	Like
6	Dislike	Like
7	Like	Dislike
8	Like	Dislike
9	Dislike	Like
10	Like	Like
11	Dislike	Like
12	Dislike	Like
13	Dislike	Like
14	Dislike	Like
15	Like	Dislike
16	Dislike	Like
17	Like	Like
18	Dislike	Like
19	Dislike	Dislike
20	Like	Dislike

Question 1: How many + signs? (0.5 pts)

Question 2: How many 0 values? (0.5 pts)

Question 3: What is the value for N?

Question 4: What is the value for x?

Question 5: Using the table, what is the p value?

Question 6: Does the use of red lights have a significant influence of liking of wine?

Answer 1

Let the dummy variable, Liking of wine = 0 if "Dislike" and 1 if "Like".

From the data values,

No Red Light	Red Light	Difference (Red - No Red)	Sign
1	1	0
0	1	1	+
0	1	1	+
0	1	1	+
1	1	0
0	1	1	+
1	0	-1	-
1	0	-1	-
0	1	1	+
1	1	0
0	1	1	+
0	1	1	+
0	1	1	+
0	1	1	+
1	0	-1	-
0	1	1	+
1	1	0
0	1	1	+
0	0	0
1	0	-1	-

1)

The number of +ve sign = 11

2)

The number of 0 values = 5

3)

The number of the total sign, N = 20 - 5 = 15

4)

X = min(-ve, +ve) = min(4,11) = 4

5)

The distribution of the sign follows the binomial distribution. The p-value is obtained from the binomial distribution table,

One-tailed P-value = 0.0592 (success of 4 or less)

6)

Let the significance level = 0.05

Since the one-tailed P-value = 0.0592 is less than the significance level = 0.05, the null hypothesis is not rejected hence we can conclude that the red lights do not have a significant influence of liking of wine