Devry MATH221 Full Course Latest 2020 April

MATH221 Statistics for Decision Making

Week 1 Homework  

Question 1The age of every fourth person entering a department store. The selected individuals would be considered a:

  Statistic

  Parameter

  Population

Correct!

  Sample

Question 2 In a survey of 1000 adults, 34% found they prefer charcoal to gas grills. The 1000 would be considered a:

  Sample

  Population

  Parameter

  Statistic

Question 3Inferential statistics is when sample data is used to:

  Influence a decision maker

  Calculate a mean

  Say something about the population

  Determine when an event is most likely to occur

Question 4The milligrams of tar in 30 cigarettes would be considered:

  Interval data

  Ratio data

  Ordinal data

  Nominal data

Question 5If a data set included the color of cars in a parking lot, those data would be considered:

  Quantitative data

  Ratio data

  Qualitative data

  Interval data

 

MATH221 Statistics for Decision Making

Week 2 Homework  

Question 1A student believes that there is a 90% probability of getting an A on the next test. This would be considered:

Empirical probability

Manufactured probability  

Subjective probability

Classical probability

Question 2Given the following information, find the probability that a randomly selected student will be tall, but not very tall. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21

50.5%

39.4%

10.1%

49.5%

Question 3Given the following information, find the probability that a randomly selected dog will be a golden retriever or a poodle. Number of dogs who are poodles: 31, golden retrievers: 58, beagles: 20, pugs: 38

46.9%

58.0%  

39.5%  

60.5%

Question 4Given that there is a 28% chance it will rain on any day, what is the probability that it will rain on the first day and be clear (not rain) on the next two days?

20.2%  

14.5%  

5.6%  

34.7%

Question 5Consider the following table. What is the probability of blue?

                Red        Blue       Green   Total

Yes         33           44           14           91

No          18           5              28           51

Total      51           49           42           142

44/49

91/142

49/142  

51/142

Question 6Consider the following table. What is probability of yes, given green?

                Red        Blue       Green   Total

Yes         33           44           14           91

No          18           5              28           51

Total      51           49           42           142

14/91

14/42

51/142

42/142

 

MATH221 Statistics for Decision Making

Week 3 Homework  

Question 1Let x represent the number of cars in a parking lot. This would be considered what type of variable:

  Discrete

  Nonsensical

  Continuous

  Lagging

Question 2 Let x represent the inches of rain on crops in Akron, Ohio. This would be considered what type of variable:

  Continuous

  Discrete

  Inferential

  Distributed 

Question 3Consider the following table.

Age Group          Frequency

18-29     9831

30-39     7845

40-49     6869

50-59     6323

60-69     5410

70 and over        5279

If you created the probability distribution for these data, what would be the probability of 40-49?

  42.5%

  23.7%

  18.9%

  16.5%

Question 4Consider the following table.

Weekly hours worked   Probability

1-30 (average=23)           0.08

31-40 (average=36)         0.10

41-50 (average=43)         0.74

51 and over (average=54)            0.08

Find the mean of this variable.

  39.0

  31.8

  41.6

  25.2

Question 5Consider the following table.

Defects in batch               Probability

0              0.28

1              0.35

2              0.16

3              0.09

4              0.10

5              0.02

Find the variance of this variable.

  0.85

  1.44

  1.35

  1.83

 

MATH221 Statistics for Decision Making

Week 4 Homework  

Question 1The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?

  Probability is 0.09, which is unusual as it is less than 5%

  Probability is 0.91, which is usual as it is greater than 5%

  Probability is 0.09, which is usual as it is not less than 5%

  Probability is 0.91, which is unusual as it is greater than 5%

Question 2Monthly water bills for a city have a mean of $108.43 and a standard deviation of $36.98. Find the probability that a randomly selected bill will have an amount greater than $165, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?

  Probability is 0.06, which is unusual as it is not less than 5%

  Probability is 0.06, which is usual as it is not less than 5%

  Probability is 0.94, which is usual as it is greater than 5%

  Probability is 0.94, which is unusual as it is greater than 5%

Question 3In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

  0.40

  Less than 1%

  0.70

  0.30

 Question 4A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.70mm. Would this outcome warrant a refund (meaning that it would be unusual)?

  Probability of 0.79 and would not warrant a refund

  Probability of 0.79 and would warrant a refund

  Probability of 0.21 and would not warrant a refund

  Probability of 0.21 and would warrant a refund 

Question 5A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 7.45 minutes with a standard deviation of 2.81 minutes.

  0.818

  0.636

  0.182

  0.018

 

 

MATH221 Statistics for Decision Making

Week 5 Homework  

Question 1 From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.69 with a population standard deviation of 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues?

  (19.24, 24.14)

  (20.71, 22.67)

  (21.78, 22.60)

  (20.86, 22.52)

Question 2If a confidence interval is given from 43.83 up to 61.97 and the mean is known to be 52.90, what is the margin of error?

  4.54

  9.07

  18.14

  43.83

Question 3If a computer manufacturer needed a supplier that could produce parts that were very precise, what characteristics would be better?

  wide confidence interval with high confidence level

  narrow confidence interval at high confidence level

  narrow confidence interval at low confidence level

  wide confidence interval with low confidence level

Question 4Which of the following are most likely to lead to a wide confidence interval?

  large sample size

  small standard deviation

  large mean

  large standard deviation

Question 5If you were designing a study that would benefit from a narrow range of data points, you would want the input variable to have:

  a small mean

  a small sample size

  a large standard deviation

  a small margin of error

 

MATH221 Statistics for Decision Making

Week 6 Homework  

Question 1A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 36 months. Write the null and alternative hypotheses and note which is the claim.

  Ho: μ ≤ 36, Ha: μ > 36 (claim)

  Ho: μ > 36, Ha: μ ≤ 36 (claim)

  Ho: μ ≤ 36 (claim), Ha: μ > 36

  Ho: μ = 36 (claim), Ha: μ ≥ 36

Question 2A business claims that the mean time that customers wait for service is at most 9.2 minutes. Write the null and alternative hypotheses and note which is the claim.

  Ho: μ ≥ 9.2, Ha: μ ≤ 9.2 (claim)

  Ho: μ > 9.2, Ha: μ ≤ 9.2 (claim)

  Ho: μ > 9.2 (claim), Ha: μ > 9.2

  Ho: μ ≤ 9.2 (claim), Ha: μ > 9.2

Question 3An amusement park claims that the average daily attendance is at least 15,000. Write the null and alternative hypotheses and note which is the claim.

  >Ho: μ ≥ 15000 (claim), Ha: μ < 15000

  Ho: μ = 15000, Ha: μ ≤ 15000 (claim)

  Ho: μ ≤ 15000, Ha: μ > 15000 (claim)

  Ho: μ > 15000 (claim), Ha: μ = 15000

Question 4A transportation organization claims that the mean travel time between two destinations is about 12 minutes. Write the null and alternative hypotheses and note which is the claim.

  Ho: μ = 12 (claim), Ha: μ ≤ 12

  Ho: μ = 12 (claim), Ha: μ ≠ 12

  Ho: μ > 12, Ha: μ ≤ 12 (claim)

  Ho: μ ≠ 12, Ha: μ = 12 (claim)

Question 5 Type I and type II errors occur because of what issue within the hypothesis testing process?

  The population is not a representative subset of the sample

  The sample mean is different than the population mean

  The sample taken is not representative of the population

  The math calculations were done incorrectly

 

 

MATH221 Statistics for Decision Making

Week 7 Homework  

Question 1Two variables have a negative non-linear correlation. Does the dependent variable increase or decrease as the independent variable increases?

  Dependent variable decreases

  Dependent variable increases

  Cannot determine from information given

  Dependent variable would remain the same

Question 2What does the variable ρ represent?

  The critical value for the correlation coefficient

  The coefficient of determination

  The sample correlation coefficient

  The population correlation coefficient

Question 3A baseball player wants to determine if the type of bat he uses each year can be used to predict the amount of improvement in his game. Which variable would be the response variable?

  The improvement in his game

  The number of times he bats

  The type of bat

  The baseball player

Question 4Two variables have a negative linear correlation. Where would the y-intercept of the regression line be located on the y-axis?

  To the right of 0

  To the left of 0

  Cannot determine

  Below 0

 

Question 5A value of the dependent variable that corresponds to the value of xi would be given the notation of:

  b

  yi

  m

  y1

 

 

MATH221 Statistics for Decision Making

Week 1 Discussion

DESCRIPTIVE STATISTICS

If you were given a large data set, such as the 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?

Alternative: Look for examples of descriptive statistics in the news or on websites.  Then post a link to that publication or site, note the statistic used and determine if it was an appropriate use of that statistic.

 

MATH221 Statistics for Decision Making

Week 2 Discussion

PROBABILITIES IN REAL WORLD

Look online and find an article published within the past 4 weeks that includes a reference to probabilities, means, or standard deviations.  These articles might be discussing weather events, investing outcomes, or sports performance, among many other possible topics.

Your first post should include a summary of the article and what numbers you are highlighting from that article.  Also include a link to the actual article.  In your replies to other students, describe specific decisions that the statistic might influence and whether a different statistic might be more appropriate.

 

MATH221 Statistics for Decision Making

Week 3 Discussion

DISCRETE PROBABILITY VARIABLES

For this discussion you will use technology to create a short 1-2 minute multimedia post/presentation.

Suggestions: Narrated PowerPoint, recorded video (.mp4), Screencast-O-Matic (.mp4), or a similar tool of your choice. Video can be recorded directly within a post as well, but make sure to plan out in advance what you are going to say/show. There should be a visual component as well as audio, so if you are using a webcam for the video that only shows you speaking, please attach your PowerPoint slide(s) (or screenshot images of them) to the post as well so everyone can see them.

In your short presentation, you will be describing an example that uses discrete probabilities or distributions. Provide an example that follows either the binomial probabilities or any discrete probability distribution, and explain why that example follows that 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.

For more information about Narrated PowerPoint, access the Student Resources section of Course Resources under the Introduction & Resources module heading, and look for the heading that corresponds to the tool you want to use. For all media posts in this course, please include a brief written synopsis to inform your classmates what the main point or purpose is that the linked, attached, or embedded media addresses.

 

MATH221 Statistics for Decision Making

Week 4 Discussion

INTERPRETING NORMAL DISTRIBUTIONS

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?

 

MATH221 Statistics for Decision Making

Week 5 Discussion

CONFIDENCE INTERVAL CONCEPTS

Look in the newspapers, magazines, and other news sources for results of a survey or poll that show the confidence interval, usually shows as a +/- some amount.  Describe the survey or poll and then describe the interval shown.  How does knowing the interval, rather than just the main result, impact your view of the results?

 

MATH221 Statistics for Decision Making

Week 6 Discussion

HYPOTHESES IN THE REAL WORLD

This is the time to start preparing for the Reflection paper at the end of the course.  As such the discussions will take on a different tone/format for weeks 6 and 7.  The posts will consist of

ANALYTICAL: Describe how you could use Hypothesis Testing to serve the needs of a decision-making process in your current job, a past job, or life situation.

GRAPHICAL: Identify two (2) options for graphically representing the data from your ANALYTICAL POST to present to decision-makers and assess the pros and cons of each graphical option.

ENGAGEMENT: Extend the conversation of another students ANALYTICAL or GRAPHICAL POST by offering another analytical method or set of graphical options.

 

MATH221 Statistics for Decision Making

Week 7 Discussion

REGRESSION

This is the time to start preparing for the Reflection paper at the end of the course.  As such the discussions will take on a different tone/format for weeks 6 and 7.  The posts will consist of

ANALYTICAL: Describe how you could use Linear Regression to serve the needs of a decision-making process in your current job, a past job, or life situation.

GRAPHICAL: Identify two (2) options for graphically representing the data from your ANALYTICAL POST to present to decision-makers and assess the pros and cons of each graphical option.

ENGAGEMENT: Extend the conversation of another students ANALYTICAL or GRAPHICAL POST by offering another analytical method or set of graphical options.

 

MATH221 Statistics for Decision Making

Week 3 Quiz   

Question 1 (CO 1) A survey of 385 people who like wild sweaters found that 74% had a wild holiday sweater. What is the population and what is the sample?

  Population: people who like wild sweaters; Sample: the 74% that had a wild holiday sweater

  Population: people who like wild sweaters: Sample: the 385 people who had a wild holiday sweater

  Population: people who like wild sweaters; Sample: the 385 people who like wild sweaters

  Population: people who like sweaters; Sample: the 74% that had a wild holiday sweater

Question 2 (CO 1) A survey of 481 of your customers shows that 79% of them like the recent changes to the product. Is this percentage a parameter or a statistic and why?

  Parameter as it represents the population

  Statistic as it represents the population !

  Statistic as it represents the sample

  Parameter as it represents the sample

Question 3 (CO 1) Classify the data of the top grossing movies for 2017.

  Classical

  Statistics

  Quantitative

  Qualitative

Question 4 (CO 1) The data set that lists the runs scored at each of the weekend’s baseball games would be classified as what type of data?

  Interval

  Ratio

  Nominal

  Ordinal

Question 5 (CO 1) A data set that includes the years in which your hometown team won championships would be classified as what type of data:

  Ratio

  Ordinal

  Interval

  Nominal

 

MATH221 Statistics for Decision Making

Week 5 Quiz   

Question 1 (CO 3) Consider the following table:

Age Group          Frequency

18-29     983

30-39     784

40-49     686

50-59     632

60-69     541

70 and over        527

If you created the probability distribution for these data, what would be the probability of 30-39?

  0.425

  0.237

Correct!

  0.189

  0.165

Question 2 (CO 3) Consider the following table of hours worked by part-time employees. These employees must work in 5 hour blocks.

Weekly hours worked   Probability

5              0.15

15           0.28

20           0.31

25           0.26

Find the mean of this variable.

  17.50

  20.60

  17.65

  18.95

Question 3 (CO 3) Consider the following table:

Defects in batch               Probability

0              0.21

1              0.28

2              0.30

3              0.09

4              0.08

5              0.04

Find the variance of this variable.

  1.67

  1.78

  1.99

  1.33

Question 4 (CO 3) Consider the following table:

Defects in batch               Probability

0              0.21

1              0.28

2              0.30

3              0.09

4              0.08

5              0.04

Find the standard deviation of this variable.

  1.41

  1.67

  1.33

  1.78

Question 5 (CO 3) Twenty-two percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have heard of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer listed below).

  0.993, 0.024

  0.024, 0.001

  0.993, 0.000

  0.024, 0.000

 

MATH221 Statistics for Decision Making

Week 7 Quiz   

Question 1 (CO 4) From a random sample of 55 businesses, it is found that the mean time that employees spend on personal issues each week is 5.8 hours with a standard deviation of 0.35 hours. What is the 95% confidence interval for the amount of time spent on personal issues?

  (5.71, 5.89)

  (5.74, 5.90)

  (5.72, 5.88)

  (5.73, 5.87)

Question 2 (CO 4)If a confidence interval is given from 8.50 to 10.25 and the mean is known to be 9.375, what is the margin of error?

  8.500

  1.750

  0.875

  0.438

Question 3 (CO 4) Which of the following is most likely to lead to a large margin of error?

  large sample size

  small sample size

  small standard deviation

  small mean

Question 4 (CO 4) From a random sample of 41 teens, it is found that on average they spend 31.8 hours each week online with a population standard deviation of 3.65 hours. What is the 90% confidence interval for the amount of time they spend online each week?

  (28.15, 35.45)

  (24.50, 39.10)

  (30.86, 32.74)

  (29.99, 33.61)

Question 5 (CO 4) A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a population standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperature of 37.37 degrees. Are the refrigerators within the 90% confidence interval?

  Yes, the temperature is within the confidence interval of (37.40, 37.60)

  No, the temperature is outside the confidence interval of (36.90, 38.10)

  Yes, the temperature is within the confidence interval of (36.90, 38.10)

  No, the temperature is outside the confidence interval of (37.40, 37.60)

 

MATH221 Statistics for Decision Making

Week 8 Assignment    

Reflection Paper

Complete the following by writing a response to three of the four following questions. For each question, your response should be 2 or more paragraphs. Make it clear which question you are answering and use correct grammar throughout. If you answer all four questions, only the first three provided will be graded.

Your responses are to be based on your own experiences and insights.  Do not use materials and examples from other sources, including the Internet.  Students have used examples from outside sources in the past and have failed this final assessment and in some cases, failed the course due to evidence of plagiarism.

Describe how you could use hypothesis testing to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, what would be the null and alternative hypotheses, and how data could ideally be collected to test the hypotheses.

Describe how you could use confidence intervals to help make a decision in your current job, a past job, or life situation. Include a description of the decision, how the interval would impact the decision, and how data could ideally be collected to determine the interval.

Describe how you could use regression analysis to help make a decision in your current job, a past job, or a life situation. Include a description of the decision, what would be the independent and dependent variables, and how data could ideally be collected to calculate the regression equation.

Describe a data set that you have encountered or could envision that would be applicable to your current job, a past job, or a life situation. Identify two (2) options for graphically representing those data to present to decision-makers, such a pie charts, time series, Pareto charts, histograms, etc. Assess the pros and cons of each graphical option.

 

MATH221 Statistics for Decision Making

Week 2 LAB   

Instructions-BEGIN

?             Data have already been formatted and entered into an Excelworksheet.

?             Obtain the data file for this lab from your instructor.

?             Use the Week 1 spreadsheet (available from the top of the Week 1 Lesson) for graphs and calculations.  You will need to copy data from the data file into the calculations spreadsheet to answer some questions.

?             The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. On page 6 of this lab, you will find a code sheetthat identifies the correspondence between the variable names and the survey questions.

?             Follow the directions below and then paste the graphs from Excel in the grey areas for question 1 through 3. You will be using the Week 1 Excel Sheet for many of the calculations.  Type your answers to questions 4 through 11 where noted in the grey areas.  When asked for explanations, please give thorough, multi-sentence or paragraph length explanations.

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