MHA 610 Quiz Part 1 and Part 2

1.      The standard deviation of the diameter at breast height, or DBH, of the slash pine tree is less than one inch. Identify the Type I error. (Points : 1)

       Fail to support the claim σ < 1 when σ < 1 is true.       Support the claim  μ < 1 when μ = 1 is true.       Support the claim σ < 1 when σ = 1 is true.       Fail to support the claim μ < 1 when μ < 1 is true.

1a.  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.

2.      Biologists are investigating if their efforts to prevent erosion on the bank of a stream have been statistically significant. For this stream, a narrow channel width is a good indicator that erosion is not occurring. Test the claim that the mean width of ten locations within the stream is greater than 3.7 meters. Assume that a simple random sample has been taken, the population standard deviation is not known, and the population is normally distributed. Use the following sample data:3.3 3.3 3.5 4.9 3.5 4.1 4.1 5 7.3 6.2What is the P-value associated with your test statistic? Report your answer with three decimals, e.g., .987 (Points : 1)

2a. 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

 Construct a 95% confidence interval estimate of the odds ratio of the odds for having Hepatitis C after Therapy 1 to the odds for having Hepatitis C after Therapy 2. Give your answer with two decimals, e.g., (12.34,56.78) (Points : 0.5)

3. 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

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)

3a. Scientists, researching large woody debris (LWD), surveyed the number of LWD pieces from aerial photos taken annually for the past 35 years at two different sites. Over the 35 years of photos examined, the first site had a mean number of LWD pieces per hectare per year (LWD/ha/yr) of 3.7 pieces with a standard deviation of 1.9. The second site had a mean number of LWD/ha/yr of 4.3 with a standard deviation of 2.4. Assume a .05 significance level for testing the claim that the mean LWD/ha at the first site had less than the mean LWD/ha/yr at the second site. Also, assume the two samples are independent simple random samples selected from normally distributed populations, but do not assume that the population standard deviations are equal.Construct a 90% confidence interval for the difference between the two means. Give your answer with two decimals, e.g., (12.34,56.78) (Points : 0.5)

4.      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)

4a. 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 predicted value of the number of new prescriptions written if $6000 is spent in regional advertising. Give your answer as an integer. (Points : 0.5)

5.      Use a .05 significance level and the observed frequencies of 70 Neonatal deaths to test the claim that number of neonatal deaths on each day of the week is equally likely. 

Mon

Tues

Wed

Thurs

Fri

Sat

Sun

10

9

5

8

15

12

11

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

5a. Use a .05 significance level and the observed frequencies of 144 drowning at the beaches of a randomly selected coastal state to test the claim that the number of drowning for each month is equally likely. 

Jan

Feb

Mar

Apr

May

June

July

Aug

Sept

Oct

Nov

Dec

1

3

2

7

14

20

37

33

16

6

2

3

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

6.      Using a .01 significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients.Gender

Male

Female

Fear Dentistry

48

70

Do Not Fear Dentistry

21

32

 Do you reject the null hypothesis, at the .01 significance level? Enter Y for yes (reject), N for no (fail to reject). (Points : 0.5)

6a. Using a .01 significance level, test the claim that the proportions of fear/do not fear responses are the same for male and female dental patients.Gender

Male

Female

Fear Dentistry

48

70

Do Not Fear Dentistry

21

32

 Determine the value of the χ2 test statistic. Give your answer to three decimals, e.g., 12.345 . (Points : 0.5)

7. 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

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

7a. The table represents results from an experiment with patients afflicted with eczema on both arms. Each patient was treated with an immune modulator cream on one arm and a topical steroid cream on the other arm. Using a .05 significance level, apply McNemar's test to test the following claim: The proportion of patients with no cure on the immune modulator treated arm and a cure on the topical steroid treated arm is the same as the proportion of patients with a cure on the immune modulator treated arm and no cure on the topical steroid treated arm. 

Immune Modulator Cream

Cure

No Cure

Topical Steroid

Cure

25

11

Cream

No Cure

42

22

 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)

8.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

 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

8a. Geneticists studying carriers of genetic diseases followed subjects subdivided by race. Researchers randomly selected seven patients per race who had been identified as carrying a certain gene for a genetic disease; these patients were followed to determine the number of their siblings who also carried the gene for the genetic disease. Use a One-Way ANOVA at a .05 significance level to test the claim that the means from the different races are not all the same. 

Caucasian

African-American

Other

2

0

0

3

0

1

3

1

2

3

2

2

4

2

2

5

2

3

5

4

4

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

9.      The reason we cannot use multiple t-tests to claim that four populations have the same mean is that we increase the likelihood of a type I error. (Points : 1)

       True       False

9a.

If there is only one observation per cell in a Two-Way ANOVA, and it can be assumed there is not an interaction between factors, then we can proceed to interpret the results of the row and column effects. (Points : 1)

       True        False 

10.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

 What is the value of the F test statistic for the site effect? (Points : 0.5)

10a. 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)