Pythagorean Theorem

In your response to your peer’s initial post comment on other variables that might potentially confound the relationship between the two displayed variables.
Peer response
Simple linear regression analyses provide a broader scope of information than correlations do. In conducting a simple linear regression, researchers are provided with several values including the slope, y-intercept, r-squared and p-value.1 In a correlation, researchers are interested in the r and p-values and these are used to determine if two variables are associated with one another, or not. Simple linear regressions assist researchers in analyzing the actual line drawn through a correlation scatterplot which can be used to predict outcomes of additional participants.

For this assignment, I am investigating the relationship between life expectancy (dependent variable) and per capita income (independent variable) in 2015. The following values were gleaned from a simple linear regression analysis conducted in Stata:
Slope = .00013
Y-Intercept = 72.42
R-squared = 0.415
P= 0.0000
The slope value tells us that for every change observed in per capita income, we can expect to see a change of .00013 in life expectancy. The y-intercept provides that with a per capita income of zero, we can expect life expectancy to be 72.42 years. The r-squared value tells us that 41.5% of the variability observed in life expectancy is due to per capita income level. Finally, the p-value tells us that we can reject the null hypothesis.1 Hypotheses in this case are as follows:

H0: Slope value = 0
H1: Slope value does not equal 0
In summary, we can use these values to predict life expectancy, given we have data for income per capita. For example, if we know a country’s per capita income in 2015 was $20,000 we can use the following equation to determine life expectancy:
Life Expectancy = 72.42 + .00013(20000)
Life Expectancy = 75.02 years

MATH 170 FINAL 1

                                                              Rating A

1. State whether the statements are true or false: AcA

A) True   B) False

2. Fill in the missing value. Assume simple interest.

principal $19,582

interest rate 4%

time ________

simple interest $2,349.84

A) time 3 years   B) time 4 years    C) time 2 years

3. Using the combination formula complete the following: How many combinations of two letters are possible from the letters U, A, and X?

A) 3    B) 5    C) 9

4. Find the probability. Write your answer as a percent rounded to the nearest whole percent: A number from 8 to 16 is drawn at random. P(12).

A) 11%    B) 13%     C) 15%

5. Evaluate the expression: 2 • 7!

A) 10,080    B) 10,280    C) 10,000

6. If A and B are independent events, P(A)=.4, and P(B)=.6 find P (A u B)

A) 0.76     B) 0.076     C) 0.0076

7. A number from 15 to 26 is drawn at random.P(24)Express the probability as a percent. Round to the nearest percent.

A) 8%     B) 9%      C) 10%

8.Evaluate the expression: 9!

A) 362880    B) 362800

9.Determine whether the events A and B are independent P(A)=.6, P(B)=.8, P(A n B)=.2

A) Independent    B) Not Independent

10.Evaluate: 3!

A) 6    B) 3     C) 1

11.Evaluate the expression: C(9,3)

A) 84     B) 48      C) 27

12.Fill in the missing value. Assume simple interest.

principal $87,698

interest rate ________

time 1 year

simple interest $6,138.86

A) interest rate 7%     B) interest rate 8%     C) interest rate 10%

13.A jar contains 21 pink and 26 navy marbles. A marble is drawn at random.P(navy)Express the probability as a decimal. Round to the nearest hundredth.

A) 0.55     B) 0.055     C) 0.0055

14.Find the probability. Assume that the spinner is separated into equal sections: You flip a coin and toss a 1-6 number cube. P(3 and heads)

A) 1/12 or 0.083     B) 1/6 or 0.167     C) 1/8 or 0.125

15. State whether the statements are true or false: {0}=0

A) True     B) False

16.Fill in the missing value. Assume simple interest.

principal $400,007

interest rate 13%

time 2 years

simple interest ________

A) simple interest $105,001.82    B) simple interest $104,001.82    C) simple interest $104,003.82

17.State whether the statements are true or false: 0eA

A) True     B) False

18.Find the probability: A number from 10 to 22 is drawn at random. P(an odd number) Express the probability as a decimal. Round to the nearest hundredth.

A) 0.46     B) 0.17     C) 0.75

19.Fill in the missing value. Assume simple interest. principal ________ interest rate 3% time 1 year simple interest $2,472.57

A) principal $82,419    B) principal $85,419    C) principal $822,419

20.There were 13,249 weddings in Springs City last year. According to state records, notaries public performed 17% of the weddings. How many weddings were not performed by notaries public?

A) 1099    B) 10994    C) 10997

21. Let A and B be two events in a sample space S such that:

(P(A)=.6,  P(B)=.5, and P(A n B).2 find P(AB)     

A) 2/5    B) 5/2

22.If A and B are independent events, P(A)=.4, and P(B)=.6 find P(A n B)

A) 0.24    B) 0.024    C) 0.0024

23.Evaluate the expression: 3•5!

A) 360   B) 120    C)15

24.Find the probability. Write your answer as a fraction in simplest form: You roll a number cube numbered from 1 to 6. P(1).

A) 1/6    B) 6    C) 1/3

25.A jar contains 25 green, 19 white, 6 pink, and 21 orange marbles. A marble is drawn at random.P(white, green, or pink)Express the probability as a fraction.

A) 50/71     B) 71/50      C) 5/7

26.Evaluate the expression: 6!+4!

A) 744     B) 704     C) 720

27.Determine whether the events A and B are independent P(A)=.3, P(B)=.6, P(A n B)=.18

A) Independent     B) Not Independent

28.Evaluate the expression: P(5,5)

A) 120    B) 230    C) 25

29.Evaluate: 5!

A) 120    B) 25    C) 5

30.Evaluate the expression: 5!-3!

A) 114    B) 2    C) 8

Consider the following findings from statistical studies:

• Smoking increases the risk of heart disease.
• Eating margarine can increase the risk of heart disease.
• One glass of wine per day can protect against heart disease but increases the risk of breast cancer.
• Potato chips and sugary sodas are the foods most strongly associated with weight gain.
You are probably familiar with some of these findings, and perhaps you’ve even altered your lifestyle as a result of them. But where do they come from? Remarkably, these and hundreds of other important findings on public health come from huge prospective studies that have provided data for hundreds of smaller statistical studies. The longest-running of these is the Harvard Nurses’ Health Study, which began in 1976 when Dr. Frank E. Speizer decided to study the long-term effects of oral contraceptives. He mailed questionnaires to approximately 370,000 registered nurses and received more than 120,000 responses. He chose to survey nurses because he believed that their medical training would make their responses more reliable than those of the general public.

As Dr. Speizer and his colleagues sifted through the data in the returned questionnaires, they realized that the study could be expanded to include more than just the effects of contraceptives. Today, this research team continues to follow many of the original 120,000 respondents.

Annual questionnaires are still a vital part of the study, allowing researchers to gather data about what the nurses eat; what medicines and vitamins they take; whether and how much they exercise, drink, and smoke; and what illnesses they have contracted. Some of the nurses also provide blood samples, which are used to measure such things as cholesterol level, hormone levels, genetic variations, and residues from pesticides and environmental pollutants. Dr. Speizer’s faith in nurses has proven justified, as they reliably complete surveys and almost always provide properly drawn and labeled blood samples upon request.

After more than three decades of correspondence, both the researchers and the nurses say they feel a sense of closeness. Many of the nurses look forward to hearing from the researchers and say that the study has helped them to pay more attention to how they live their lives. Today, as the original nurses become elderly, the study is beginning to turn out results that should shed light on factors that influence longevity and health in old age.

The success of the Harvard Nurses Study has spurred its expansion and many similar studies of large groups. When you see statistical reports based on these studies, remember the hundreds of thousands of people whose willingness to participate in these studies is making life better for everyone.

QUESTIONS FOR DISCUSSION

Read the “Focus on Public Health: Is your Lifestyle Healthy” article found on page 44 at the end of Chapter 1. 
For this week’s Discussion, you will discuss some of the points made in this article. Answer the following questions for your initial main post. 

1. Consider some of the results that are likely to come from the Harvard Nurses’ Health Study over the next 10 to 20 years. What types of results do you think will be most important? Do you think the findings will alter the way you live your life? 
   
2. Explain why the Harvard Nurses’ Health Study is an observational study and not an experiment. Why do you think this is and discuss whether it would be possible to gather similar data by carrying out experiments in a practical and ethical way? 
   
3. The Harvard Nurses’ Health Study is subject to participation bias because only 120,000 of the original 370,000 questionnaires were returned. Should the researchers be concerned about this bias? Do you think that dishonesty can affect this type of observational study? Why or why not? 
   
4. What is the population of interest for this study? What is the sample? Does the population include males? Do you think that the results can be used to make direct inferences about men? Why or why not? 

Demonstrate the use of the normal distribution, the standard normal distribution, and the central limit theorem for calculating areas under the normal curve and exploring these concepts in real life applications.

Instructions

Student Profile

Frank has only had a brief introduction to statistics when he was in high school 12 years ago, and that did not cover inferential statistics. He is not confident in his ability to answer some of the problems posed in the course.

Concept Being Studied

Finding areas and probabilities by using the standard normal distribution and the Z-Table.

As Frank’s tutor, you need to provide Frank with guidance and instruction on a worksheet he has partially filled out. Your job is to help him understand and comprehend the material. You should not simply be providing him with an answer as this will not help when it comes time to take the test. Instead, you will be providing a step-by-step breakdown of the problems including an explanation on why you did each step and using proper terminology.

What to Submit

To complete this assignment, you must first download the worksheet, and then complete it by including the following items on the worksheet:

• Incorrect Answers
• Correct any wrong answers. You must also explain the error performed in the problem in your own words.
• Partially Finished Work
• Complete any partially completed work. Make sure to provide step-by-step instructions including explanations.
• Blank Questions
• Show how to complete any blank questions by providing step-by-step instructions including explanations.

Your step-by-step breakdown of the problems, including explanations, should be present within the answers provided on the document.