08 Jan 2. A company that makes colas

MATH399 Week 1 Discussion Latest 2017 March

Descriptive Statistics (graded)

If you were given a large data set (i.e., sales over the last year of our top 100 customers), what might you be able to do with these data? What might be the benefits of describing the data?

For additional videos, Excel templates, voice video on excel templates, How to work with ilabs please refer to this webpage

Math 399 – Supplemental class material (weblink)

Here are a few questions from Chapter 1 & 2 study plan that you can practice and also participate for discussion points. This will help you towards understanding the concepts and also prepare you toward the Week 3 Quiz. Please work on only one question at a time and give opportunities to your classmates to work on the questions. You can learn and lend a helping to your classmates, share technology help and links to understand, suggestions and tips..Remember homework alone is not sufficient to prepare toward quizzes. Therefore it is important that you practice in the study plan . Answers will be posted on Saturday evening.

1. Determine whether the given value is a statistic or a parameter.

A sample of students is selected and it is found that 35% own a computer

Study plan 1.1.41

2. Determine whether the underlined numerical value is a parameter or statistic. Explain your reasoning.

A certain zoo found that 8% of its 843 animals were nocturnal

Study Plan: 1.1.37

3. Suppose a survey of 568 women in the United States found that more than 56% are the primary investor in their household. Which part of the survey represents the descriptive statistics? Make an inference based on the results of the survey.

4. How is a sample related to a population?

5. Determine whether the variable is qualitative or quantitative

a. Goals scored in a hockey game

b. Favorite musical instrument

Study plan 1.2.7

6. What is an inherent Zero? Describe an example that has an inherent zero.

Study plan 1.2.31

7. Which method of data collection should be used to collect data for the following study.

A study of the health of 164 kidney transplant patients at a hospital.

Study plan 1.3.11

8. Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits and the upper class limits.

Minimum = 13, maximum = 84, 6 classes

Study plan 2.1.11

9. Some graph questions to study: Study Plan 2.1.19, 2.1.26, 2.1.27

10. Students in an experimental psychology class did research on depression as sign of stress. A test was administered to a sample of 30 students. The scores are shown below.

43 50 10 90 77 35 64 36 42 72

54 62 35 75 50 72 36 29 39 61

48 63 35 41 21 36 50 46 86 14

a. Find the 10% trimmed mean of the data.

b. Find Mean

c. Find Median

D. Find Mode

E. Midrange

Please use the paste to clipboard from the data set to work in excel or in minitab

Study plan 2.3.65

11. Find the range, mean, variance and standard deviation of the sample data set.

7 10 17 15 5 11 16 6 13

Study plan 2.4.13

MATH399 Week 2 Discussion Latest 2017 March

Regression (graded)

Suppose you are given data from a survey showing the IQ of each person interviewed and the IQ of his or her mother. That is all the information that you have. Your boss has asked you to put together a report showing the relationship between these two variables. What could you present and why?

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For additional videos, Excel templates, voice video on excel templates, How to work with ilabs please refer to this webpage

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Here are a few questions that you can participate for discussion points from your study plan on correlation and regression. This may help you toward understanding concepts and also in the quiz for Week 3. Please work on only one question at a time. Answers will be posted on Saturday morning. Please download the file that has data.

I have attached Excel worksheet under “excel forum”. Delete the data from the cells and enter your data for graphing scatter plot, finding correlation and regression equation.

1. Construct a scatter plot and determine the type of correlation using r for the following data

The ages(in years) of 6 children and the number of words in their vocabulary

Age, x

1

2

3

4

5

6

Vocabulary size,y

250

950

1200

1450

1800

2650

a) Display the data in a scatter plot

b) Calculate the correlation coefficient r

c) Make a conclusion about the type of correlation

Study plan 9.1.22, 9.1.24

2. Suppose the scatter plot shows the results of a survey of 42 randomly selected males ages 24 to 35. Using age as the explanatory variable, choose the appropriate description for the graph, Explain your reasoning.

a) Age and body temperature

b) Age and balance on student loans

c) Age and income

d) Age and height

PLEASE SEE THE DOCUMENT ATTACHED FOR THIS GRAPH

The response variable is ____________ because you would expect this variable and age to have _________________ and ____________variation for adult males.

Study plan 9.2.17

3. Identify the explanatory and the response variable.

A farmer wants to determine if the temperature received by similar crops can be used to predict the harvest of the crop.

The explanatory variable is _________

The response variable is ____________

4. Find the equation of the regression line for the given data. The construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

Hours spent studying,x

Test score, y

0

41

2

42

3

49

4

47

4

64

5

67

a. Find the regression equation.

b. Scatter plot

c. Predict the value of y for x= 2

d. Predict the value of y for x=3.5

e. Predict the value of y for x= 12

MATH399 Week 3 Discussion Latest 2017 March

Probability and Odds (graded)

The odds of winning a game are given as 1:25. What is the probability that you will win this game? What is the probability that you will lose this game? In your follow-up replies, consider which number in the odds ratio needs to change and how it needs to change in order to increase the probability of winning. (Note: See page 145 in the text for a discussion on odds.)

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For additional videos, Excel templates, voice video on excel templates, How to work with ilabs please refer to this webpage

CLICK HERE FOR ALL EXCEL WORKSHEETS AND YOUTUBE LINKS

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PLEASE COMPLETE THE QUIZ THIS WEEK that covers WEEK 1 and WEEK 2 that covers Week 1 and Week 2 material only.

Here are a few questions that you can participate for discussion points from your study plan on correlation and regression that may help you toward understanding concepts and the quiz for Week 5. Please work on only one question at a time. Answers are posted at the end of the questions.

PROBABILITY DISTRIBUTIONS

Objective – CONCEPTS:

1. Determine which of the following numbers could not represent the probability of an event

0, 0.008, -0.6, 65%, 715/1206, 60/47

Study plan: 3.1.1, 3.1.2, 3.1.7, 3.1.8

Objective-Sample Space

2. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.

Determining a person’s grade Freshman (F), Sophomore (So), Junior (J), Senior (Se) and gender (male(M) Female (F))

Study Plan: 3.1.15, 3.1.17, 3.1.19

Objective-Simple Events

3. Determine the number of outcomes in the event. Decide whether the event is a simple event or not.

You randomly select one card from a standard deck. Event A is selecting a red four.

Study Plan: 3.1.21, 3.1.23

Objective-Frequency Distribution

4. Use the frequency distribution below, which shows the number of voters (in millions) according to age, to find the probability that a voter chosen at random is in the given age range.

Not between 25 and 34 years old

Ages of voters

Frequency

18 to 20

7.4

21 to 24

11.5

25 to 34

21.8

35 to 44

25.5

45 to 64

56.8

65 and over

28.7

Study Plan: 3.1.55, 3.1.57, 3.1.59, 3.1.61, 3.1.63

Objective-Distinguish between independent and dependent events

5. Researchers found that people with depression are four times more likely to have a breathing-related sleep disorder that people who are not depressed. Identify the two events described in the study. Do the results indicate that the events are independent or dependent?

Study Plan: 3.2.7, 3.2.11, 3.2.13, 3.2.15

Objective-Conditional Probability

6. In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 600 carries a mutation of the BRCA gene. Seven out of 10 women with this mutation develop breast cancer.

a. Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.

b. Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.

c. Are the events of carrying this mutation and developing breast cancer independent or dependent events.

Study Plan: 3.2.17, 3.2.27

Objective-Multiplication Rule to Find Probabilities

7. A study found that 38% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-two percent of the ART pregnancies resulted in multiple births.

a. Find the probability that a randomly selected ART cycle resulted in a pregnancy and produced a multiple birth.

b. Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.

c. Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth? Explain

Study Plan: 3.2.21, 3.2.23, 3.2.26

Objective-Mutually exclusive

8. Decide if the events are mutually exclusive.

Event A: Randomly selecting someone treated with a certain medication.

Event B: Randomly selecting someone who received no medication

Study Plan: 3.3.7, 3.3.9, 3.3.11

Objective-Addition Rule

9. During a 52-Week period, a company paid overtime wages for 16 Weeks and hired temporary help for 8 Weeks. During 4 Weeks, the company paid overtime and hired temporary help.

a. Are the events “Selecting a Week that contained overtime wages” and “selecting a Week that contained temporary help wages” mutually exclusive

b. If an auditor randomly examined the payroll records for only one Week, what is the probability that the payroll for that Week contained Overtime wages or temporary help wages?

Study Plan: 3.3.13, 3.3.15, 3.3.17,3.3.25

MATH399 Week 4 Discussion Latest 2017 March

Discrete Probability Variables (graded)

Provide an example that follows either the binomial or Poisson distribution, and explain why that example follows that particular distribution. In your responses to other students, make up numbers for the example provided by that other student, and ask a related probability question. Then, show the work (or describe the technology steps), and solve that probability example.

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For selected homework questions, additional videos, Excel templates, voice video on excel templates, How to work with ilabs please refer to this webpage

CLICK HERE FOR ALL EXCEL WORKSHEETS AND YOUTUBE LINKS

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OFFICE HOUR recording Link – we discussed how to use excel templates to do week 4 lab and hwk.

https://dvg.webex.com/dvg/lsr.php?RCID=38ea17328cd90f55e9c01d2d735b1146

Here are a few questions that you can participate for discussion points from your study plan on discrete probabilities that may help you toward understanding concepts and the quiz for Week 5. Please work on only one question at a time. Look for the Answers posted on Saturday Evening.

Definitely use the excel worksheet

OBJECTIVE: IS THE EXPERIMENT A BINOMIAL EXPERIMENT?

1. About 40% of babies born with a certain ailment recover fully. A hospital is caring for seven babies with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment? If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

STUDY PLAN: 4.2.9, 4.2.11

OBJECTIVE: Find the MEAN, VARIANCE AND STANDARD DEVIATION OF THE binomial distribution

2. Find the mean, variance and standard deviation of the binomial distribution n= 123, p= 0.69

STUDY PLAN: 4.2.15

OBJECTIVE: FIND BINOMIAL PROBABILITIES USING TECHNOLOGY

3. 47% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is

a. Exactly eight

b. At least eight

c. Less than eight

STUDY PLAN: 4.2.19, 4.2.21, 4.2.23, 4.2.25

OBJECTIVE: FIND PROBABILITIES FOR POISSON DISTRIBUTION USING technology

4. Given that x has a Poisson distribution with mean mu= 4, what is the probability that x= 6?

STUDY PLAN: 4.3.5

MATH399 Week 5 Discussion Latest 2017 March

Interpreting Normal Distributions (graded)

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

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For homework questions, additional videos, Excel templates, voice video on excel templates, How to work with ilabs please refer to this webpage

CLICK HERE FOR ALL EXCEL WORKSHEETS AND YOUTUBE LINKS

Recorded office hour link toward quiz for week #5.

https://dvg.webex.com/dvg/lsr.php?RCID=f167284e6723643995d35d9aac2b1972

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Here are a few questions that you can participate for discussion points from your study plan on normal distribution that may help you toward understanding concepts and the quiz for Week 7. Please work on only one question at a time. Answers are posted at the end.

OBJECTIVE: CONCEPTS

1. What requirements are necessary for a normal probability distribution to be a standard normal distribution?

STUDY PLAN: 5.1.2, 5.1.3, 5.1.7

OBJECTIVE: COMPUTE AND INTERPRET Z-SCORES of NORMAL DISTRIBUTIONS

2. The systolic blood pressures of a sample of adults are normally distributed, with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 122, 113, 106 and 128 millimeters of mercury. The graph of the standard normal distributions is shown below. Complete a) and b) PLEASE SEE ATTACHED DOCUMENT FOR GRAPHS

a. Without converting to z scores, match the values with the letters A, B, C, and D on the given graph of the standard normal distribution.

b. Find the z-score that corresponds to each value and check your answers to part (a) (Round to two decimals as needed)

STUDY PLAN: 5.1.41, 5.1.43

OBJECTIVE: FIND PROBABILITIES USING THE STANDARD NORMAL DISTRIBUTION

3. For the standard normal distribution shown below, find the probability of z occurring in the indicated on the graph. Please see attached document

STUDY PLAN: 5.1.45, 5.1.47, 5.1.55, 5.1.57

OBJECTIVE: FIND PROBABILITIES FOR NORMALLY DISTRIBUTED VARIABLES

4. Assume the random variable x is normally distributed with mean mu= 50 and

standard deviation sigma= 7. Find P(x > 42)

STUDY PLAN: 5.2.1, 5.2.3, 5.2.5, 5.2.7, 5.2.9, 5.2.11, 5.2.15

OBJECTIVE: APPLICATIONS OF NORMAL DISTRIBUTION

5. Use the normal distribution of SAT writing scores with mean = 493 and standard deviation = 111.

a. What percentage of SAT writing scores are less than 600?

b. If 1000 SAT writing scores are randomly selected, about how many would you expect to be greater than 550?

STUDY PLAN: 5.2.21, 5.2.23, 5.2.25, 5.2.27

OBJECTIVE: FIND A Z SCORE GIVEN THE AREA UNDER THE NORMAL CURVE

6. Find the z score that corresponds to the cumulative area of 0.049

STUDY PLAN: 5.3.1, 5.3.3, 5.3.5, 5.3.7, 5.3.17, 5.3.19, 5.3.21, 5.3.23, 5.3.25, 5.3.27, 5.3.29

OBJECTIVE: APPLICATION OF NORMAL DISTRIBUTION

7. In a survey of women in a certain country (ages 20- 29), the mean height was 65.3 inches with a standard deviation of 2.67 inches.

a. What height represents the 98th percentile?

b. What height represents the first quartile?

STUDY PLAN: 5.3.31, 5.3.33, 5.3.35, 5.3.38, 5.3.39, 5.3.41

OBJECTIVE: Interpret sampling distributions

8. A population has a mean mu= 86 and a standard deviation sigma =20. Find the mean and standard deviation of a sampling distribution of sample means with a sample size n= 268

STUDY PLAN: 5.4.1, 5.4.3

OBJECTIVE: CENTRAL LIMIT THEOREM

9. Use the central limit theorem to find the mean and standard error of the mean of the sampling distribution.

The mean price of photo printers on a website is $221 with a standard deviation of $69. Random samples of size 34 are drawn from the population and the mean of each sample is determined. (ROUND ANSWERS TO THREE DECIMALS)

10. The population mean annual salary for environmental compliance specialists is about $61,500. A random sample of 34 specialists is drawn from this population. What is the probability that the mean salary is less than $59,000? Assume standard deviation sigma= $5800?

MATH399 Week 6 Discussion Latest 2017 March

Confidence Interval Concepts (graded)

Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you

increase the confidence level,

increase the sample size, or

increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula.

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For few homework questions, additional videos, Excel templates, voice video on excel templates, How to work with ilabs please refer to this webpage

CLICK HERE FOR ALL EXCEL WORKSHEETS AND YOUTUBE LINKS

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PLEASE USE THE Z SCORE FOR THE GIVEN CONFIDENCE LEVEL if you are working the problems by hand.

Here are a few questions that you can participate for discussion points from your study plan on normal distribution. This may help you toward understanding concepts and the quiz for Week 7.

Please see attached excel worksheet for calculations if you are interested.

OBJECTIVE: FIND THE MARGIN OF ERROR

1. Find the margin of error for the given values of c = 0.95 , s= 3.6 and n= 36

(Round to three decimal places as needed)

STUDY PLAN: 6.1.13, 6.1.15

OBJECTIVE: CONSTRUCT AND INTERPRET CONFIDENCE INTERVALS FOR THE POPULATION MEAN

2. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 37 gas grills has a mean price of $637.70 and a standard deviation of $58.30

(Round to one decimal place as needed)

STUDY PLAN: 6.1.35, 6.1.36, 6.1.37, 6.1.40

OBJECTIVE: DETERMINE THE MINIMUM SAMPLE SIZE

3. A doctor wants to estimate the HDL cholesterol of all 20- to 29- year-old females. How many subjects are needed to estimate the HDL cholesterol within 4 points with 99% confidence assuming standard deviation sigma = 19.4? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required?

(Round to the next whole number)

STUDY PLAN: 6.1.53, 6.1.56

4. A 2011 Gallup Poll found that 76% of Americans believe that high achieving high school students should be recruited to become teachers. This poll was based on a random sample of 1002 Americans.

a. Find a 95% confidence interval for the proportion of Americans who would agree to this.

b. Interpret your result in the context of the given study.

c. Do these data refute a pundit’s claim that 2/3 of Americans believe this statement? Explain.

Taken from Stats Data & Models. De Veaux velleman Bock 4th edition

OBJECTIVE: DETERMINE THE MINIMUM SAMPLE SIZE

5. A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed Internet access. Her estimate must be accurate within 2% of the true proportion.

a. Find the minimum sample size needed, using a prior study that found that 52% of the respondents said they have high-speed Internet access.

(Round to the nearest whole number as needed)

b. What is the minimum sample size needed assuming that no preliminary estimate is available?

STUDY PLAN: 6.3.17, 6.3.18

MATH399 Week 7 Discussion Latest 2017 March

Rejection Region (graded)

How is the rejection region defined, and how is that related to the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?

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For a few hwk questions. additional videos, Excel templates, voice video on excel templates, How to work with ilabs please refer to this webpage

CLICK HERE FOR ALL EXCEL WORKSHEETS AND YOUTUBE LINKS

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PLEASE PARTICIPATE IN THE BELOW QUESTIONS. Do take the quiz in Week 7 that covers only on Week 5 & Week 6 early on in the week.

OBJECTIVE: WRITE THE NULL AND ALTERNATIVE HYPOTHESES. IDENTIFY WHICH IS THE CLAIM

1. A study claims that the mean survival time for certain cancer patients treated immediately with chemotherapy and radiation is 16 months.

STUDY PLAN: 7.1.29, 7.1.30

OBJECTIVE: TEST A CLAIM ABOUT A MEAN USING CRITICAL VALUES

2. A company that makes colas drinks states that the mean caffeine content per 12-ounce bottle of cola is 45 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 43.3 milligrams with a standard deviation of 6.8 milligrams. At alpha = 0.05, can you reject the company’s claim?

STUDY PLAN: 7.2.35, 7.2.37

OBJECTIVE: TEST THE CLAIM FOR PROPORTIONS USING REJECTION REGION

3. A humane society claims that less than 35% of U.S households owns a dog. In a random sample of 409 U.S households, 154 say they own a dog. At alpha =0.10, is there enough evidence to support the society’s claim?

STUDY PLAN: 7.4.15, 7.4.17