# Mathematics

The EPA claims that fluoride in children’s drinking water should be at a mean level of less than 1.2 ppm, or parts per million, to reduce the number of dental cavities. Identify the Type I error. (Points : 1)

Fail to support the claim σ < 1.2 when σ < 1.2 is true.

Support the claim μ < 1.2 when μ = 1.2 is true.

Support the claim σ < 1.2 when σ = 1.2 is true.

Fail to support the claim μ < 1.2 when μ < 1.2 is true.

Question 2 of 10 Medical researchers studying two therapies for treating patients infected with Hepatitis C found the following data. Assume a .05 significance level for testing the claim that the proportions are not equal. Also, assume the two simple random samples are independent and that the conditions np ≥ 5 and nq ≥ 5 are satisfied.

Therapy 1

Therapy 2

Number of patients

39

47

Eliminated Hepatitis

20

13

C infection

Find the z test statistic. Give your answer with two decimals, e.g., 9.87 . (Points : 0.5)

Researchers studying sleep loss followed the length of sleep, in hours, of 10 individuals with insomnia before and after cognitive behavioral therapy (CBT). Assume a .05 significance level to test the claim that there is a difference between the length of sleep of individuals before and after CBT. Also, assume the data consist of matched pairs, the samples are simple random samples, and the pairs of values are from a population having a distribution that is approximately normal.

Individual

1

2

3

4

5

6

7

8

9

10

Before

6

5

4

5

3

4

5

3

4

2

CBT The paired data consist of the cost of regionally advertising (in thousands of dollars) a certain pharmaceutical drug and the number of new prescriptions written (in thousands).

Cost

9

2

3

4

2

5

9

10

Number

85

52

55

68

67

86

83

73

Find the value of the linear correlation coefficient r . Give your answer to three decimals, e.g., .987 . (Points : 0.5)

Use a .05 significance level and the observed frequencies of 144 drownings at the beaches of a randomly selected coastal state to test the claim that the number of drownings for each month is equally likely.

Jan 1

Feb 3

Mar 2

Apr 7

May 14

June 20

July 37

Aug 33

Sept 16

Oct 6

Nov 2

Dec 3

Determine the value of the χ2 test statistic. Give your answer to two decimals, e.g., 12.34 . (Points : 0.5)

Using a .01 significance level, test the claim that the proportions of people who favor/oppose pro-choice on the abortion issue are the same for the males and females.

Gender

Male

Favor Pro-Choice

65

120

Female

Oppose Pro-Choice

42

38

Determine the value of the χ2 test statistic. Give your answer to two decimals, e.g., 12.34 . (Points : 0.5)

The table represents results from an experiment with patients afflicted in both eyes with glaucoma. Each patient was treated in one eye with laser surgery and in the other eye was treated with eye drops. Using a .05 significance level, apply McNemar’s test to test the following claim: The proportion of patients with no improvement on the laser treated eye and an improvement on the drops treated eye is the same as the proportion of patients with an improvement on the laser treated eye and no improvement on the drops treated eye.

Eye Drop Treatment

Improvement

No Improvement

Laser Surgery

Improvement

15

10

Treatment

No Improvement

50

25

Do you reject the null hypothesis, at the .05 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5)

For a study on Type 1 diabetes, medical graduate students subdivided the United States into four study regions (Northeast, Southeast, Southwest, and Northwest). The students randomly selected seven patients per region and recorded the number of times during a randomly selected month that each patient used insulin shots to regulate blood sugar levels. Use One-Way ANOVA at a .05 significance level to test the claim that the means from the different regions are not the same.

Mean number of times patients used insulin shots to regulate blood sugar levels

Northeast

Southeast

Southwest

Northwest

4

6

4

4

3

5

5

4

3

6

6

5

4

8

6

6

3

6

7

3

2

6

5

5

5

8

4

3

Determine the value of the F test statistic. Give your answer to two decimals, e.g., 12.34 . (Points : 0.5)

Assuming calculations for a One-Way ANOVA with equal sample sizes, if each data value in one of the samples is increased by a fixed amount, then any change in the F test statistic and the P-value is attributable only to the change in the sample variances. (Points : 1)

True

False

Use the following technology display from a Two-Way ANOVA to answer this question. Biologists studying habitat use in Lepidopteran moths measured the number of savannah moths found at three randomly selected prairie sites with two potential habitat interferences (expansion of row crops and grazing). Use a .05 significance level.

Source

Df

SS

MS

F

P

Site

2

.1905

.0952

.0381

.9627

Habitat

1

304.0238

304.0238

121.6095

.0000

Site*Habitat

2

.1905

.0952

.0381

.9627

Do you reject the null hypothesis about the site effect, at the .05 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5)

After

8

8

7

6

7

6

6

5

7

5

CBT

Construct a 95% confidence interval estimate of the mean difference between the lengths of sleep. Give your answer with two decimals, e.g., (12.34,56.78) (Points : 0.5)