Statistics
Directions: Before you begin, save this form (FILE, SAVE AS: M8A2_Final Exam_Your First and Last Name). Read scenarios 1 – 8, and then answer questions 1—50. In order to receive full credit, you must copy and paste a screen captured image of your data output file from the statistical software that was used to compute the answer. To generate a screen capture image, press ALT + Prt Scr. Save your work frequently to your computer. Once you are ready to submit your work, click Browse My Computer and find your file. Once you’ve located your file click Open and, if successful, the file name will appear under the Attached files heading. Scroll to the bottom of the page, click Submit and you’re done. Be sure to check your work and correct any spelling or grammatical errors before you post.
Scenario 1:
General Questions- Answer the following multiple choice questions (1-10). Type out your answer in the space provided, include both the letter and the selection.
As the length of the confidence interval for the population mean increases, the degree of confidence in the interval’s actually containing the population mean_________________?
A Stay the same
B Increases
C Decreases
D Doubles
Answer: _______________
What value of a correlation coefficient indicates that there is a perfect positive relationship between the dependent variable, y, and the independent variable, x?
Answer: ___________
What value of a correlation coefficient indicates that there is no relationship between the dependent variable, y, and the independent variable, x?
Answer: ___________
For a fixed level of confidence when the sample size increases, the length of the confidence interval for a population mean will______________?
A Stay the same.
B Increase.
C Decrease.
D Doubles.
Answer: ___________
Which of the following confidence intervals will be the widest?
A 90 Percent.
B 95 Percent.
C 98 Percent.
D 80 Percent.
Answer: ___________
The probability of failing to detect an effect when one exists is known as a:
A Type II error.
B Type I error.
C Standard error.
D Standardized erro.r
Answer: ___________
Concluding that there is an effect when in reality no effect exists is known as a:
A Type II error.
B Type I error.
C Standard error.
B Type I error.
Answer: _________
As the sample size increases, how is the power of the study affected?
A It is not affected.
B It is decreased.
C It approaches zero.
D It is increased.
Answer: ___________
When a researcher decreases the risk of making a type 1 error, the risk of making a type II error is?
A Decreased.
B Not Affected.
C Increased.
D Equal to the chance of making a type I error.
Answer: ___________
The coefficient of determination
A helps establish causal relationships.
B indicates the amount of variance that two variables share.
C is the same as the correlation coefficient.
D is equivalent to standard deviation.
Answer: ___________
Scenario 2:
To determine the effectiveness of a new anti-hypothyroid drug, circulating thyroid stimulating hormone (TSH) levels were measured in 20 men (with hypothyroid levels) and compared to 20 men (with hypothyroid levels) that received current standard therapy as control. The data are summarized in the table below.
What is the null hypothesis equation for this experiment?
Answer: ___________
Based on the statistical test that you chose, do you accept or reject the null hypothesis at P=0.05?
Answer: ___________
What is the 95% confidence intervals for this 2 sample t-test?
Answer: ___________
What is the difference of Means?
Answer: ___________
What is the expected standard deviation (s) within groups?
s = “SEM Difference of means” /√(1/n+1/n) Round to the thousandths place.
Answer: ___________
What is the Power of this test? Please paste your data output file in the area below.
Answer: ___________
Assuming that the difference of means and expected standard deviation within groups remain the same, how many samples are needed to achieve a power of 0.80? Alpha=0.05.
Answer: ___________
Scenario 3.
An insurance company is interested in determining if the severity of a burn increases the length of hospitalization for burn patients. Their data is summarized in the table below.
Patient # Burn Severity
(Percent of body burnt x the degree of burn) Burn
Rank
Length of Hospital Stay (hours) Hospital Stay
Rank
1 1.33 1 74.1 2
2 1.25 2 74.2 1
3 1.22 3 73.5 3
4 1.11 4 72.5 4
5 1.1 5 72.1 5
6 0.99 6 58 6
7 0.95 7 56 7
8 0.88 8 48 8
9 0.8 9 38.1 9
10 0.7 10 32.2 10
11 0.56 11 28.2 11
12 0.4 12 25 12
13 0.35 13 24.5 13
14 0.32 14 24.6 14
15 0.3 15 24 15
What statistical test would be appropriate to establish a relationship between burn severity [Burn degree (1st degree, 2nd degree, and 3rd degree) x percent of body burned] and the duration of hospitalization expressed by the number of days?
A Pearson Product-Moment Correlation coefficient
B Multiple Regression
C ANOVA
D Spearman Rank Correlation coefficient.
Answer: ___________
What is the correlation coefficient?
Answer: ____________
Please paste your data output file in the space below.
Is the correlation positive or negative?
Answer: ___________
Scenario 4:
Have you noticed the abundance of television ads for yogurt that contain probiotics? Probiotics are live micro-organisms which, when administered in adequate amounts, confer a health benefit on the host. Your body needs to have a healthy amount of ”good” bacteria in the digestive tract. Many yogurts are made using active, good bacteria. A diabetes researcher hypothesized that ratio good bacteria in the digestive tract would be decreased in people that are overweight. The results are summarized in the table below.
What type of statistical test would you use to determine if there is an association between the ratio of good bacteria and BMI?
Multiple linear Regression
ANOVA
Pearson Product-Moment Correlation Coefficient
Spearman Rank Correlation Coefficient
Answer: ___________
Do you accept or reject the null hypothesis that there is no relationship between BMI and the ratio of good bacteria in the digestive tract at the significance level P=0.05? Please paste your data output file in the space below.
Answer: ___________
Scenario 5:
The data in the following table show the relationship of cholesterol level in men to the risk of a heart attack. The data are summarized in the table below.
What is the slope and intercept of the regression line?
Answer: ___________
What type of statistical test would you use to determine if there is an association between cholesterol levels and the risk of a heart attack?
A Multiple linear Regression
B ANOVA
C Pearson Product-Moment Correlation Coefficient
D Spearman Rank Correlation Coefficient
Answer: ___________
Is the correlation positive or negative?
Answer: ___________
What is the correlation between cholesterol levels and the risk of suffering a heart attack?
Answer: ___________
What is the coefficient of determination for the value in the previous question? Round to the thousandths place.
Answer: ___________
Scenario 6
Suppose that you wanted to determine if a dietary supplement is effective at lowering blood pressure. You randomly select 200 people with slightly elevated blood pressure and give them either a placebo or the dietary supplement. Your research design is as follows in Table 1. You randomly select 100 people to receive the dietary supplement, and 100 people to receive the placebo. In order to determine the effectiveness of the dietary supplement, you measure systolic blood pressure. The drug was considered a success if it reduced blood pressure levels below 130 mm Hg. Your research hypothesis is: The dietary supplement will reduce blood pressure compared to placebo in people with moderately high blood pressure levels.
Table 1. Dietary Supplements and Lowering Blood Pressure
Blood pressure below 130mmHg Blood Pressure above 130 mm Hg
Placebo
n=100 20 people 80 people
Dietary Supplement
N=100 30 people 70 people
What is the null hypothesis equation for this experiment?
Answer: ___________
What proportion of people that received the placebo control had their blood pressure reduced at the end of the study?
Answer: ___________
What proportion of people that received the placebo control had their blood pressure reduced at the end of the study?
Answer: ___________
What statistical test would you use?
A 2 proportion z-test
B ANOVA
C Relative Risk
D 2 sample t-test
Answer: ___________
Based on the statistical test you chose, do you accept or reject the null hypothesis at P=0.05? Please paste your data output file in the area below.
Answer: ___________
What is the 95% confidence interval for this experiment?
Answer: ___________
What is the power of this statistical test? Please paste your data output file in the space below.
Answer: ___________
Assuming that the expected proportions remain the same for the two groups, how many samples are needed to achieve a power level of 0.80?
Answer: ___________
Which of the following statements is correct about why you would use the Yates continuity correction when performing a Power analysis?
A To increase your chances of making a type I error.
B To decrease your chances of making a type I error.
C To increase your chances of making a type II error.
D To decrease your chances of making a type II error.
Answer: ___________
Scenario 7
A research team wanted to determine if there is an association between an artificial sweetener and developing bladder cancer. They randomly selected individuals into the exposure group (Healthy individuals that consume artificial sweetener in diet soda; 1 L/day) and compare them to a randomly selected control group (Healthy individuals that do not consume artificial sweetener; 1L/day). They followed the subjects for a period of time 10 years. The data are summarized in the table below.
Table 2. Artificial Sweetener and Bladder Cancer
Developed Bladder Cancer Did Not Develop Bladder Cancer
Consume Artificial sweetener 75 325
Do Not Consume Artificial sweetener 50 350
What is the null hypothesis equation for this experiment?
Answer: ___________
What is the value of n for each group?
Answer: ___________
What statistical test would you use?
A 2 proportion z-test
B ANOVA
C Relative Risk
D 2 sample t-test
Answer: ___________ Risk
Based on the statistical test you chose, do you accept or reject the null hypothesis at P=0.05? Please paste your data output file in the area below
Answer: ___________
What is the 95% confidence interval for this experiment?
Answer: _____________
What is the power of this statistical test? Please paste your data output file in the area below
Answer: ___________
Assuming that the expected relative risk and expected proportion in unexposed controls remained the same, how many samples are needed to achieve a power level of 0.80? Please paste your data output file in the area below
Answer: ___________
Scenario 8:
Marijuana is the second most commonly smoked substance next to tobacco worldwide. With the recent legalization of marijuana in Colorado, a study was done to examine the relationships between chronic obstructive pulmonary disease (COPD) and smoking marijuana. Six hundred cases of males between the ages of 18 and 29 that reported to have smoked marijuana on their routinely on health physical examinations were cross matched for COPD. Six hundred age matched males were used as controls. The data are summarized in Table 3 below.
Table 3. Marijuana and Chronic Obstructive Pulmonary Disease
Develop chronic obstructive pulmonary disease (COPD) Do not Develop chronic obstructive pulmonary disease (COPD) Total
Smokes only Marijuana 81 519 600
Non smoker 58 542 600
What is the null hypothesis equation for this experiment?
Answer: _______________
What statistical test would you use?
A z-test
B ANOVA
C Relative Risk
D Odds ratio
Answer: _______________
Based on the statistical test you chose, do you accept or reject the null hypothesis at P=0.05? Please paste your data output file in the area below.
Answer: _______________
What is the 95% confidence interval for this experiment?
Answer: _______________
What is the expected proportion of controls for this experiment? Round to the thousandths place.
Answer: _______________
What is the power of this experiment? Please paste your data output file in the area below.
Answer: _______________
Assuming that the expected odds ratio and expected proportion in unexposed controls remained the same, how many samples are needed to achieve a power level of 0.80? Please paste your data output file in the area below.