MATH 170 FINAL 1

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

 

 

Homework Assignment 7.3

Class Section

Homework Assignment 7.3
18 points
Print out this assignment and write your name on it and turn it in instead of answering the
questions on notebook paper. You may print front and back if you wish. Be sure to include your
first name and last name. Put your class section number on the area of the line above “Class
Section”.
Problems 1 – 6: Find the function f (x) that will make the given equation an identity. The
function f (x) may be a trig function, algebraic function, or constant function.
Each problem has a solution. Simplify all answers.
1.

cos(2x)
= f 2(x)
1 – tan2(x)

2.

f (x) = _______________________

3.

cos2(x)
1 – 1 + sin(x) = f (x)

1 + cos(2x)
= f (x)
sin(2x)

f (x) = _______________________

cos(x)
= f (x)
1 + sin(x)

f (x) = __________________________

4.

f (x) = _______________________

5.

tan(x) +

 x
 x
tan   + cot   = 2 f ( x)
2
2

f (x) = ___________________________

6.

cos(x)
1 + sin(x)
+
= 2f (x)
1 + sin(x)
cos(x)

f (x) = ___________________________

Problems 7 – 11: Verify each identity. Provide all necessary details.
7.

sec2(θ) csc2(θ) = sec2(θ) + csc2(θ)

8.

cos(2θ)
= cos(θ) – sin(θ)
cos(θ) + sin(θ)

9.

tan(θ )
θ 
tan   =
 2  sec(θ ) + 1

10. sin(2θ) =

2 tan(θ)
1 + tan2(θ)

11. sin(2x) – tan(x) = tan(x) cos(2x)

Problems 12 – 14:

Show that each of the following is not an identity.

12. cos(2θ) = 2cos(θ) sin(θ)

 t  sin(t )
13. sin   =
2
2

14. cos(2t) = 2cos(t)

Problems 15 and 16: Write each of the following as a product of trig functions. Simplify your
answers.
15. sin(6θ) + sin(3θ)

Answer: _________________________________________________________________

16. cos(5θ) – cos(θ)

Answer: __________________________________________________________________

Problems 17 and 18: Write each of the following as a sum or difference of trig functions.
Simplify your answers.

17. sin(6θ) sin(3θ)

Answer: _________________________________________________________________

18. cos(5θ) cos(θ)

Answer: _________________________________________________________________

MAth Hypothesis testing

(1) Collect 50 or more qualitative data items. Use the same method of collecting 50 or more data items that you used in the Module 1 discussion. You may use the same data you used in Module 6. You will first construct an appropriate set of hypotheses, H0 and H1, regarding your data. This might involve doing research regarding your data beforehand to figure out a meaningful set of hypotheses.

View an example on how to use StatCrunch (with data) to do hypotheses tests for a population proportion.

Then, answer the following five parts:

  1. Write down the null hypothesis.
  2. Write down the alternative hypothesis.
  3. Explain why you chose your hypotheses as such.
  4. Do a hypothesist test of your data at the α = 2% level of significance for the population proportion by carrying out the following five steps:
    1. View an example of how to use StatCrunch to compute the value Zα 
      If it is a left-tailed test, what is the critical value, –z0.02?
      If it is a right-tailed test, what is the critical value, z0.02?
      If it is a two-tailed test, what are the two critical values, ±z0.01?
    2. Write down the test statistic, z0.
    3. Write down the P-value.
    4. Write down the sample size.
    5. Write down the sample porportion.
    6. Use the classical method to reach your conclusion on whether or not to accept or reject the null hypothesis. Be sure to explain how you reached your conclusion.
    7. Use the P-value to reach your conclusion on whether or not to accept or reject the null hypothesis. Be sure to explain how you reached your conclusion.
  5. Does the conclusion make sense to you? why or why not?

Hypotheses

This is for a disscussion board. 

 

Share with your peers the null and alternative hypotheses for a decision that is relevant to your life. This can be a personal item or something at work. Be sure that it is mathematical in nature.  Additionally, identify the Type I and Type II Errors that could occur with your decisionmaking process. Be sure to quantify your hypotheses as much as possible and identify your variables.

 

For example, suppose a newspaper article stated that the average weight of cats is 5 lbs. Suppose you think that the average weight of cats is more than 5 lbs. Then the hypotheses are:

H0: μ < 5
Ha:  μ >5
Here  μ is the population average weight of cats. This would be an example of an Upper Tail test.

 

************************************
************************************

A way of understanding hypothesis testing is to think of a court case:
Suppose Joe is accused of stealing an expensive diamond. Then there are 2 hypotheses:

H0: Joe is innocent (H0 is the assumption, the status quo, innocent until proven guilty)
H1: Joe is guilty (the alternative hypothesis)

The goal of the prosecutor is to collect evidence so that the judge switches over from H0 to H1.

You are assuming H0 is true. Thus, the goal of the prosecutor is to collect convicting evidence so compelling that it is very unlikely for an innocent person to have.

For example, it is very unlikely that an innocent person is found with the stolen diamond in hand, a video camera showing Joe near the scene, a map in Joe’s home of the Jewelry store,…,etc.

Since this is very unlikely to happen to an innocent person, the judge switches over by rejecting H0, innocent.

You want to the probability of convicting an innocent person to be small.
i.e. you want to minimize the probability of rejecting H0 given that H0 is true (Minimize the probability of a Type I error).

This can be written as the following conditional probability:
small= P( rejecting H0 | H0 is true) = the probability of convicting an innocent person

The probability above is called the probability of a Type I error. It is denoted with the Greek letter alpha.

P(Type I error) = P( rejecting H0 | H0 is true) = alpha
The statistician decides what alpha will be.

For example, the judge might draw the line at alpha=.001.

i.e.
.001= P( rejecting H0 | H0 is true) = the probability of convicting an innocent person.

Alpha is the borderline probability between innocent and guilty.

i.e. If Joe is assumed to be innocent and the evidence collected against him has a probability of less than .001 occurring, then the judge will reject H0 and accept Ha (guilty).

Regression analysis

Question 1 Assignment: Data needed for questions 3-7 at bottom of page:

In a regression analysis with multiple dependent variables, multicollinearity can be caused by:

A strong nonlinear relationship between the dependent variable and one or more independent variables.

A strong heteroskedastic relationship between the dependent variable and one or more independent variable.

A strong linear relationship between two or more independent variables.

None of the above.

Question 2 
Market researcher Ally Nathan is studying the relationships among price, type (classical or steel string), and consumer demand for acoustic guitars. She wants to find the relationship between demand and price, controlling for type.
To determine this relationship, she should

Run a simple regression of the dependent variable demand on the independent variable price and observe the coefficient on price. 

Run a simple regression of the dependent variable demand on the independent variable type and observe the coefficient on type. 

Run a multiple regression of the dependent variable demand on the independent variables price and type and observe the coefficient on type. 

Run a multiple regression of the dependent variable demand on the independent variables price and type and observe the coefficient on price. 

Question 3 
The regression analysis relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars”.
The coefficient on the independent variable tells us that:

For every additional dollar of GDP, average energy consumption increased by 3,786 trillion BTUs.

For every additional trillion dollars of GDP, average energy consumption increased 3,786 BTUs. 

For every additional trillion BTUs of energy consumption, average GDP increased by $3,786 trillion. 

For every additional trillion dollars of GDP, average energy consumption increased by 3,786 trillion BTUs. 

Question 4 
The regression analysis relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars”.
Which of the following statements is true?

The y-intercept of the regression line is 62,695 trillion BTUs. 

The x-intercept of the regression line is $62,695 trillion.

In the event that a thermonuclear war completely halts all economic activity and the US GDP drops to zero, energy consumption will sink to 62,695 trillion BTUs. 

None of the above. 

Question 5 
The regression analysis relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars”. 
In a given war, if GDP is $7.4 trillion, expected energy consumption is:

Around 91,501 trillion BTUs

Around 90,711 trillion BTUs 

Around 28,016 trillion BTUs

Around 467,729 trillion BTUs.

Question 6 
The regression analysis relates US annual energy consumption in trillions of BTUs to the independent variable “US Gross Domestic Product (GDP) in trillions of dollars”.
How much of the variation in energy consumption can be explained by variation in the gross domestic product?

About 99.99%

About 97%

About 94%

Almost none of the variation in energy consumption can be explained by variation in GDP. 

Question 7 
The data table at the bottom of the page tabulates a pizza paror’s advertising expenditures and sales for 8 consecutive quarters. The marketing manager wants to know how much of an impact current advertising will have on sales two quarters from now.
While running a regression with the dependent variable “sales” and the independent variable “advertising lagged by two quarters”, how many data points can she use, given the available data?

9

For questions 3 through 6:
Year GDP 
(in $trillions) Car Gas Mileage (in mpg) Energy Consumption 
( in trillions of BTU)
1980 2.796 16 78,435
1981 3.131 16.5 76,569
1982 3.259 16.9 73,441
1983 3.535 17.1 73,317
1984 3.933 17.4 76,972
1985 4.213 17.5 76,705
1986 4.453 17.4 76,974
1987 4.743 18 79,481
1988 5.108 18.8 82,994
1989 5.489 19 84,926
1990 5.803 20.2 84,567
1991 5.986 21.1 84,640
1992 6.319 21 86,051
1993 6.642 20.5 87,780
1994 7.054 20.7 89,571
1995 7.401 21.1 91,501
1996 7.813 21.2 94,521
1997 8.318 21.5 94,969
1998 8.782 21.6 95,338
1999 9.274 21.4 96,968

US Energy Consumption (in trillion BTUs)
vs. Gross Domestic Product ($trillions)

Regression Statistics
Multiple R 0.9709
R2 0.9426
Adjusted R2 0.9394 F test results
Standard Error 1,889 F value Signif. F
Observations 20 295.51 0.0000 

Coefficients Std Error t Stat P-value
Intercept 62,695 1,325 47.31 0.0000 
GDP ($trillions) 3,786 220 17.19 0.0000 

For Question #7:

Quarter Sales (in $) Advertising (in $)
Qtr 1, 2001 523,000 88,000
Qtr 2, 2001 512,000 84,000
Qtr 3, 2001 528,000 92,000
Qtr 4, 2001 533,000 92,000
Qtr 1, 2002 540,000 96,000
Qtr 2, 2002 540,000 95,000
Qtr 3, 2002 538,000 93,000
Qtr 4, 2002 541,000 98,000

bua math qrb501 wk3 qu-1

Business Math, Ch. 7

Why is the standard deviation big?

As you probably already know from your reading, standard deviation indicates the spread of the data. There can be many reasons that data has a big spread. Some common reasons are:

 

1.  That’s just the way the data happens.  An example of this would be if we were randomly choosing men anywhere in the world and measuring their height.  The possibility exists that we would choose the world’s tallest man and/or the world’s shortest man to include in our data. These heights would make our numbers look weird, but in fact, they are correct.

 

2.  There is a problem with the data.  This can happen for many reasons:

  • The measurement was not done properly
  • miscalibrated machinery
  • The wrong units were used (years rather than days, net income versus gross income, etc.)
  • The respondents in our sample misunderstood the question.  One example of this from my business would be when we asked a question about “talk shows” we did not anticipate that a large part of our sample would consider morning shows on music stations as “talk shows.”
  • The procedure for measurement has changed over a period of time (for example, the way Autism is diagnosed has changed over the year, so including data from years past may not be accurate).
  • Machinery is more sensitive and/or sophisticated and can now measure more and better than before.  For instance, now we are able to detect earthquakes and measure different attributes of hurricanes than we were in the 1800s.
  • There is a typo in our data.
  • The interviewer (in the case of an in-person interview) misunderstood the respondent’s answer, or recorded it incorrectly.

3.  There is an underlying variable that is causing variation in our data.  An example of this would be with our DJ example above. Most likely, the DJ with the higher standard deviation has a polarizing personality that causes one gender to like the DJ while the other does not, or the DJ appeals to a younger audience rather than an older audience, etc.   Another common example here would be if we were in retail looking at the number of transactions for a store, an underlying variable that we would need to account for before beginning the analysis would be that there are different sizes of stores.

 

Of course the lists above are not exhaustive, so there are more reasons, but these are some main points.  Have you encountered any of these scenarios in your job? If so, please share your experience with the class.

QNT/351 WEEK 2 Probability Worksheet

Complete the Probability Worksheet.

Format your paper consistent with APA guidelines.

Click the Assignment Files tab to submit your assignment.

 

University of Phoenix Material                          

 

PROBABILITY

 

Maximum and Minimum Temperatures

 

 

Search the Internet for U.S. climate data.

 

Choose the city in which you live. 

 

Click on the tab that reads “Daily.” 

 

  1. Prepare a spreadsheet with three columns:  Date, High Temperature, and Low Temperature.  List the past 60 days for which data is available.

 

  1. Prepare a histogram for the data on high temperatures and comment on the shape of the distribution as observed from these graphs.

 

  1. Calculate and S. 

 

  1. What percentage of the high temperatures are within the interval  – S to + S?

 

  1. What percentage of the high temperatures are within the interval  – 2S to + 2S?

 

  1. How do these percentages compare to the corresponding percentages for a normal distribution (68.26% and 95.44%, respectively)?

 

  1. Repeat Parts 2 to 6 for the minimum temperatures on your spreadsheet. 

 

  1. Would you conclude that the two distributions are normally distributed?  Why or why not?

 

 

MAT 510 ASSIGNMENT 7 (USE AS A GUIDE)

The experiment data in below table was to evaluate the effects of three variables on invoice errors for a company. Invoice errors had been a major contributor to lengthening the time that customers took to pay their invoices and increasing the accounts receivables for a major chemical company. It was conjectured that the errors might be due to the size of the customer (larger customers have more complex orders), the customer location (foreign orders are more complicated), and the type of product. A subset of the data is summarized in the following Table.

 

Table: Invoice Experiment Error

Customer Size

Customer Location

Product Type

Number of Errors

16

+

19

+

4

+

+

2

+

21

+

+

25

+

+

17

+

+

+

22

Customer Size: Small (-), Large (+)

Customer Location: Foreign (-), Domestic (+)

Product Type: Commodity (-), Specialty (=)

 

Reference: Moen, Nolan, and Provost (R. D. Moen, T. W. Nolan and L. P. Provost. Improving Quality through Planned Experimentation. New York: McGraw-Hill, 1991)

 

Use the date in table above and answer the following questions in the space provided below:

1.     Identify the effects of the factors studied in this experiment? Which are most important? Why?

2.     What strategy would you use to reduce invoice errors, given the results of this experiment?

Assignment 2: Statistics

Due in Week 3 and worth 30 points

The following data consists of the actual time used and potential (the best time possible for this review process) to complete each step in the review process. The actual times are based on the review of 30 projects. The potential times are subjective engineering judgment estimates.

Use the data in the table above and answer the following questions in the space provided below:

  1. What are the sources of value-added and non-value-added work in this process?
  2. Where are the main opportunities to improve the cycle time of this process, with respect to both actual time used and the potential best times? What strategy would you use?
  3. Step 10: Resolve Open Issues required 104 hours (potential) versus 106 hours (actual). Is there an OFI here? Why or why not? If so, how would you attack it?
  4. What do you think are the most difficult critical issues to deal with when designing a sound cycle time study such as this one?

Download the homework below, type your answers into the d

 

 

 

 

Homework Assignment 3

Due in Week 3 and worth 30 points

 

The following data consists of the actual time used and potential (the best time possible for this review process) to complete each step in the review process. The actual times are based on the review of 30 projects. The potential times are subjective engineering judgment estimates.

 

Table: Basic Data Review for Construction Project Equipment Arrangement

 

 

 

Cycle Time (hours)

 

Step

Description

Actual

Potential

Difference

1

Read basic data package

4

4

2

Write, type, proof, sign, copy, and distribute cover letter

21.9

0.5

21.4

3

Queue

40

0

40

4

Lead engineer calls key people to schedule meeting

4

0.25

3.75

5

Write, type, proof, sign, copy, and distribute confirmation letter

25.4

2.1

23.3

6

Hold meeting; develop path forward and concerns

4

4

7

Project leader and specialist develop missing information

12

12

8

Determine plant preferred vendors

12

12

9

Review notes from meeting

12

12

10

Resolve open issues

106

104

2

11

Write, type, proof, sign, copy, and distribute basic data acceptance letter

26.5

0.25

26.25

 

Totals

267.8

151.1

116.7

Use the data in the table above and answer the following questions in the space provided below:

1.     What are the sources of value-added and non-value-added work in this process?

2.     Where are the main opportunities to improve the cycle time of this process, with respect to both actual time used and the potential best times? What strategy would you use?

3.     Step 10: Resolve Open Issues required 104 hours (potential) versus 106 hours (actual). Is there an OFI here? Why or why not? If so, how would you attack it?

4.       What do you think are the most difficult critical issues to deal with when designing a sound cycle time study such as this one?

 

Type your answers below and submit this file in Week 3 of the online course shell:


 

 

Assignment 1: Bottling Company Case Study

Assignment 1: Bottling Company Case Study

 

Due Week 10 and worth 140 points

Imagine you are a manager at a major bottling company. Customers have begun to complain that the bottles of the brand of soda produced in your company contain less than the advertised sixteen (16) ounces of product. Your boss wants to solve the problem at hand and has asked you to investigate. You have your employees pull thirty (30) bottles off the line at random from all the shifts at the bottling plant. You ask your employees to measure the amount of soda there is in each bottle. Note: Use the data set provided by your instructor to complete this assignment. 

Bottle Number

Ounces

Bottle Number

Ounces

Bottle Number

Ounces

1

14.23

11

15.77

21

16.23

2

14.32

12

15.80

22

16.25

3

14.98

13

15.82

23

16.31

4

15.00

14

15.87

24

16.32

5

15.11

15

15.98

25

16.34

6

15.21

16

16.00

26

16.46

7

15.42

17

16.02

27

16.47

8

15.47

18

16.05

28

16.51

9

15.65

19

16.21

29

16.91

10

15.74

20

16.21

30

16.96


Write a two to three (2-3) page report in which you:

  1. Calculate the mean, median, and standard deviation for ounces in the bottles.
  2. Construct a 95% Confidence Interval for the ounces in the bottles.
  3. Conduct a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Clearly state the logic of your test, the calculations, and the conclusion of your test.
  4. Provide the following discussion based on the conclusion of your test:  

a. If you conclude that there are less than sixteen (16) ounces in a bottle of soda, speculate on three (3) possible causes. Next, suggest the strategies to avoid the deficit in the future.

Or

b. If you conclude that the claim of less soda per bottle is not supported or justified, provide a detailed explanation to your boss about the situation. Include your speculation on the reason(s) behind the claim, and recommend one (1) strategy geared toward mitigating this issue in the future.

Your assignment must follow these formatting requirements:

  • Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.  No citations and references are required, but if you use them, they must follow APA format.