1.Fabrics respond differently to the same dye. Clothing manufacturers need to be able to match the colors of different fabrics. A researcher dyed samples of cotton and of ramie with a dye called procion blue, applied in the same way to each sample. Then she measured the lightness of the color with a colorimeter on a scale in which black is 0, white is 100. Here are the data for 8 pieces of each fabric.

Cotton: 48.82 48.88 48.98 49.04 48.68 49.34 48.75 49.12

Ramie: 41.72 41.83 42.05 41.44 41.27 42.27 41.12 41.49

Evidently one procedure gives darker colors than the other. Make a confidence interval estimate for the mean darkness of cotton minus the mean darkness of ramie after this dye procedure. Use 96% as your confidence level.

Lower Confidence Level:

Upper Confidence Level:

2.A psychology professor asked her sophomore students "Does either of your parents allow you to drink alcohol around him or her?" and when drinking (not necessarily around your parent) "How many drinks do you typically have per session?" (For these purposes, a drink is defined as a 12 oz. beer, a 4oz. glass of wine, or a one oz. shot of liquor.)

The next tables contains the responses from female students who are not abstainers.

Drinks per session for students whose parent allows them to drink

2.5 1 2.5 3 1 3 3 3 2.5 2.5 3.5 5 2

7 7 6.5 4 8 6 6 3 6 3 4 7 5

3.5 2 1 5 3 3 6 4 2 7 5 8 1

6 5 2.5 3 4.5 9 5 4 4 3 4 6 4

5 1 5 3 10 7 4 4 4 4 2 2.5 2.5

Drinks per session for students whose parents do not allow them to drink

9 3.5 3 5 1 1 3 4 4 3 6 5 3

8 4 4 5 7 7 3.5 3 10 4 9 2 7

4 3 1

If you treat these two samples as SRSs, do they provide significant evidence at the 3% level that the behavior of the parents affects how many drinks the students have on average?

Formulate H0H0 and HaHa.

a. Give the test statistic:

b. Give the PP-value:

3.A psychology professor asked her sophomore students "Does either of your parents allow you to drink alcohol around him or her?" and when drinking (not necessarily around your parent) "How many drinks do you typically have per session?" (For these purposes, a drink is defined as a 12 oz. beer, a 4oz. glass of wine, or a one oz. shot of liquor.)

The next tables contains the responses from female students who are not abstainers.

Drinks per session for students whose parent allows them to drink

2.5 1 2.5 3 1 3 3 3 2.5 2.5 3.5 5 2

7 7 6.5 4 8 6 6 3 6 3 4 7 5

3.5 2 1 5 3 3 6 4 2 7 5 8 1

6 5 2.5 3 4.5 9 5 4 4 3 4 6 4

5 1 5 3 10 7 4 4 4 4 2 2.5 2.5

Drinks per session for students whose parents do not allow them to drink

9 3.5 3 5 1 1 3 4 4 3 6 5 3

8 4 4 5 7 7 3.5 3 10 4 9 2 7

4 3 1

If you treat these students as an SRS, construct a 92% confidence interval for the population proportion of sophomore college students at least one of whose parents allows them to drink around him or her. Do both the large sample and the plus four procedure.

Large Sample:

Lower confidence level:

Upper confidence level:

Plus four method:

Lower confidence level:

Upper confidence level:

4.A cracker bakery wants to test microwaving crackers after breaking to reduce the risk of broken crackers at the time the package is opened.

The experimenter randomly assigns 65 crackers from one day's production to be microwaved after baking, and another 65 to a control group. Fourteen days later, 3 of the microwaved crackers show visible "checking", which is the starting point for breaks. At the same time, 57 of the 65 crackers in the control group show signs of checking.

Do these samples provide evidence significant at the 2% level that microwaving after baking reduces the risk of checking in these crackers?

Formulate H0H0 and HaHa.

a. Give the test statistic:

b. Give the PP-value:

5.Two different protocols for treating breast cancer were compared. One, called ALND, involves more radical surgery (more tissue is removed) with a greater risk of side effects. The other, called SLND, involves less tissue removal and possibly fewer side effects. (There is more detail about this study on p. 526 of Moore, Notz and Fligner, 6th Edition.)

A group of patients is randomly assigned to one or the other treatment and the patients are followed up after five years to see if they are still disease free at that point. The results are summarized in the following table.

Group Sample size Disease free after five years

ALND 420 345

SLND 436 366

Do ths study provide evidence significant at the 2% level that the proportions of patients who are cancer free after five years are different under the two treatments?

Formulate H0H0 and HaHa.

a. Give the test statistic:

b. Give the PP-value:

6.You construct a confidence interval of the form

0.26720p0.44978

from a sample of size 102 with 36 successes using the "plus 4" procedure.

Give the confidence level.

Confidence level: