Question

A group of experts has rated your winery’s two best varietals. Ratings are on a scale from 1 to 20, with higher numbers being better. The results are shown in Table 1.

Expert	Chardonnay	Cabernet Sauvignon	Expert	Chardonnay	Cabernet Sauvignon
1	17.8	16.6	6	19.9	18.8
2	18.6	19.9	7	17.1	18.9
3	19.5	17.2	8	17.3	19.5
4	18.3	19.0	9	18.0	16.2
5	19.8	19.7	10	19.8	18.6

a. Is this a paired or unpaired situation? Why?

c. Find the appropriate standard error for the average difference.b. Find the average rating for each varietal and the average difference in ratings (Chardonnay minus Cabernet Sauvignon).

d. Find the 95% two-sided confidence interval for the mean difference in rating.

e. Test to see if the average ratings are significantly different. If they are significantly different?

Answer 1

(a)

Here data is unpaired because experts has rated your winery’s two best varietals.

(b)

Following table shows the calculations:

Expert	Chardonnay, x1	Cabernet Sauvignon, x2	(x1-x1mean)^2	(x2-x2mean)^2
1	17.8	16.6	0.6561	3.3856
2	18.6	19.9	1E-04	2.1316
3	19.5	17.2	0.7921	1.5376
4	18.3	19	0.0961	0.3136
5	19.8	19.7	1.4161	1.5876
6	19.9	18.8	1.6641	0.1296
7	17.1	18.9	2.2801	0.2116
8	17.3	19.5	1.7161	1.1236
9	18	16.2	0.3721	5.0176
10	19.8	18.6	1.4161	0.0256
Total	186.1	184.4	10.409	15.464

Sample size

Mean:

The average difference in ratings is:

(c)

Standard deviation:

The pooled standard deviation:

-------------

So standard error for difference in population mean is

(d)

Degree of freedom for t is df=10+10-2=18

The critical value of t using excel function "=TINV(0.05,18)" is 2.101.

The confidence interval is:

(e)

Since confidence interval contains zero so we cannot conclude that they are significantly different.