Traditionally, wine has been sold in glass bottles with cork stoppers. The stoppers are supposed to keep air out of the bottle because oxygen is the enemy of the wine. Particularly red wine. Recent research appears to indicate that metal screw caps are more effective in keeping air out of the bottle. However, metal caps are perceived to be inferior and usually associated with cheaper brands of wine. A random sample of 130 people who drink at least one bottle per week on average was asked to participate in an experiment. All were given the same wine in two types of bottles. One group was given a corked bottle, and the other group of people was given a bottle with a metal cap and asked to taste the wine and indicate what they think the retail price of the wine should be.

Consider the bottles with a cork stopper as population 1 and the bottles with a metal cap as population 2.

Cork price	Metal price
16	13
10	12
15	16
10	5
17	7
11	8
14	6
13	10
11	11
14	9
11	6
16	16
18	15
16	15
10	9
17	17
14	6
14	10
16	11
7	7
10	8
12	11
19	22
15	21
16	11
14	6
9	11
12	10
21	17
13	12
10	13
16	11
12	16
16	18
13	12
17	11
17	11
13	8
14	8
18	18
11	5
12	5
15	9
16	10
13	9
18	14
16	8
17	9
12	8
12	7
14	6
9	12
11	12
14	15
19	19
13	4
11	6
17	15
11	9
13	5
15	15
14	9
18	8
18	6
18	7
12	5
10	12
11	4
13	16
14	15
11	6
14	11
18	17
13	7
13	5
19	16
17	13
14	12
17	17
17	17
18	9
19	19
21	19
12	2
15	15
16	5
15	13
10	7
10	11
17	15
12	14
14	9
16	10
12	11
13	6
17	19
17	19
13	10
15	7
12	9
14	10
16	18
15	15
15	16
15	8
12	11
18	13
13	14
12	11
15	7
10	7
13	5
11	7
16	15
14	13
10	6
15	17
14	12
15	12
12	15
16	9
11	13
17	21
16	17
10	5
15	17
11	12
19	14
15	14
20	13

1. What is the point estimate? Show the formula used to calculate it

2. Estimate the standard deviation of the difference of the sample means.

3. Calculate the degrees of freedom

4. State the null and the alternative hypotheses. Is it left-tailed, right tailed or two tailed test? Why?

5. Determine the rejection and nonrejection regions. Alpha=0.05 What is (are) the Critical value (s) ? 6. Calculate the value of the test statistic. Show the formula used to calculate it.

7. Make a decision

8. The 95% confidence interval is:

8.1 Lower Confidence Limit= (Show the formula used to calculate it.)

8.2 Upper Confidence Limit= (Show the formula used to calculate it.)