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MAT 300
M&Ms® Project
Part 5 (3 pts)
Using the methods in Section 8.4, test the hypothesis (a = 0.05) that the population proportions of red and brown are equal (pred = pbrown). You are testing if their proportions are equal to one another, NOT if they are equal to one another AND equal to 13%. NOTE: These are NOT independent samples, but we will use this approach anyway to practice the method. This also means that n1 and n2 will both be the total number of candies in all the bags. The “x” values for red and brown are the counts of each we found on the Data page. You will need to calculate the weighted p:
Be sure to state clear hypotheses, test statistic, critical value or p-value, decision (reject/fail to reject), and conclusion in English. Submit your answer as a Word, Excel, .rtf or .pdf format through the M&M® project link in the weekly course content.
HELP
You can use StatCrunch or the TI to help with this test. Needed information for both tools include:
x1 = number of red
n1 = total number of candies
x2 = number of brown
n2 = total number of candies
For the TI, you will want 2-PropZTest. Then select the appropriate alternative (not equal), and Calculate then enter. The output will have the test statistic (z), p-value (p), sample p values, weighted p (), then repeat of sample sizes.
For StatCrunch, you will select Stat > Proportions > Two Sample > with summary. The output will contain the test statistic (Z-Stat) and p-value.
Additional help is available in the Online Math Workshop under MAT300 Archived Workshop. Specifically Two Sample Inferences and Using Technology – Two Sample.
At the end of this project, you will be writing a report, explaining the method and presenting the results from each part of the project. You might find it useful to write this as you complete the work, so the report will be mostly written by the time it is assigned.
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Sheet3
Sheet2
Sheet1
Gender
Age
# people in household
Favorite TV sport
Eye color
Own / Rent
Height (inches)
Shoe size
Female
26-30
Football
Green
Rent
Male
31-35
None, I don’t watch sports
Brown
36-40
55-60
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]]>Eliminate t to determine what type of conic is described by the parametric equations:
(a) , .
(b) ,
(c) ,
Convert the polar equation to rectangular form and identify:
3. Find an equation for the parabola whose focus is at (-2,6) and whose directrix is the line y = -2.
What are the coordinates of the vertex?
Draw a graph of the parabola.
Find an equation for the parabola with horizontal axis of symmetry if it passes through the points (5,0), (14,1), and (5,-2).
5.
Eliminate t to determine what type of conic is described by the parametric equations:
(a) , .
(b) ,
(c) ,
Convert the polar equation to rectangular form and identify:
3. Find an equation for the parabola whose focus is at (-2,6) and whose directrix is the line y = -2.
What are the coordinates of the vertex?
Draw a graph of the parabola.
Find an equation for the parabola with horizontal axis of symmetry if it passes through the points (5,0), (14,1), and (5,-2).
5. For the conic whose equation is
Identify the conic:
Complete the square and write the conic in standard form:
Sketch the graph:
Find an equation for the ellipse whose graph is
y
End points of major axis (2,-3) and (2,9).
Length of minor axis: 6.
______________________x
Identify and graph the conic:
(b)
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola:
(a)
(b)
(c)
(d)
Identify and graph the conic:
(b)
Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola:
(a)
(b)
(c)
(d)
3. Find an equation for the parabola whose focus is at (-2,6) and whose directrix is the line y = -2.
What are the coordinates of the vertex?
Draw a graph of the parabola.
Find an equation for the parabola with horizontal axis of symmetry if it passes through the points (5,0), (14,1), and (5,-2).
5. For the…
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Part 2 Summary
Data
Blue
Orange
Green
Red
Yellow
Brown
Histogram
Sample size
Number of bags sampled
Number of candies sampled
bin
Num. of Candies in Bag
Sample mean number of candies per bag
Sample Standard deviation of mean number of candies per bag
x
p
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MAT 300
M&Ms® Project
Part 4 (21 pts)
Use the M&Ms® data to complete this assignment. You will be using the methods of 7.4 for the color proportions and 7.2 for the mean number of candies per bag. For the Bonus you will be using the methods of 7.5.
You can use StatCrunch to assist with the calculations. A link for StatCrunch can be found under Tools for Success in Course Home. Here is also a link: http://statcrunch.pearsoncmg.com/statcrunch/larson_les4e/dataset/index.html. You can also find additional help on both confidence intervals and StatCrunch in the Online Math Workshop under Tab: “MAT300 Archived Workshops”. Specifically you will be looking for Hypothesis Tests and Using Technology – Hypothesis Testing.
Submit your answers in Excel, Word or pdf format. Submit your file through the M&M® project link in the weekly course content. Be sure to state clear hypotheses, test statistic values, critical value or p-value, decision (reject/fail to reject), and conclusion in English (what does reject/fail to reject the null mean in terms of your hypotheses). When doing calculations for the color proportions, keep at least 4-6 decimal places sample proportions, otherwise you will encounter large rounding errors.
Masterfoods USA states that their color blends were selected by conducting consumer preference tests, which indicated the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, they claim the following percentages of colors for M&Ms® milk chocolate candies: 24% blue, 20% orange, 16% green, 14% yellow, 13% red and 13% brown.
3 pts. Test their claim that the true proportion of blue M&Ms® candies is 0.24 at the 0.05 significance level.
3 pts. Test their claim that the true proportion of orange M&Ms® candies is 0.20 at the 0.05 significance level.
3 pts. Test their claim that the true proportion of green M&Ms® candies is 0.16 at the 0.05 significance level….
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]]>Here is an assignment using minitab and some statistics i need help with.
MBA 501A â [STATISTICS]
ASSIGNMENT 3
INSTRUCTIONS: Please note that point allocation varies per question.
Use the Help feature in MINITAB 16 to read descriptions for the data sets so that you can make meaningful comments.
[15 pts] 1. Use the data set PULSE.MTW.
Construct a 95% confidence interval for the proportion of students who smoke regularly. [5 pts]
Construct a 99% confidence interval for the proportion of students who smoke regularly. [5 pts]
Interpret your results. [5 pts]
[20 pts] 2. Use the data set UGRADSURVEY.MTW in the Student 14 folder.
At , test whether at least 75% of students download songs over the internet. Explain your results. [10 pts]
At , test whether more than 10% of students participate in chat rooms over the internet. Explain your results. [10 pts]
[10 pts] 3. Use the data set ENDOWMENT.MTW in the Student14 folder.
Test whether the average endowment is at least $2,250,000. Use .
[15 pts] 4. Use the data file RESTRNT.MTW.
Construct a 95% confidence interval for the mean number of full-time employees. [5 pts]
Construct a 95% confidence interval for the mean number of seats in the dining area. [5 pts]
Interpret your results. [5 pts]
[20 pts] 5. Use the data file ASSESS.MTW in the Student14 folder.
At , test whether at least 10% of homes are Bi-level (Height). Explain your results. [10 pts]
At , test whether the mean acreage is 1.5 acres. Explain your results. [10 pts]
[20 pts] 6. Use the data file UGRADSURVEY.MTW in the Student 14 folder.
At , test whether the average number of times logged onto the internet each day is at least 5. Explain your results. [10 pts]
At , test whether the average number of minutes logged onto the internet each day is at least 200. Explain your results. [10 pts]
2
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]]>Using MINITAB perform the regression and correlation analysis for the data on INCOME (Y, the dependent variable) and CREDIT BALANCE (X, the independent variable) by answering the following.
1.Generate a scatterplot for INCOME vs. CREDIT BALANCE, including the graph of the “best fit” line. Interpret.
2.Determine the equation of the “best fit” line, which describes the relationship between INCOME and CREDIT BALANCE.
3.Determine the coefficient of correlation. Interpret.
4.Determine the coefficient of determination. Interpret.
5.Test the utility of this regression model (use a two tail test with =.05). Interpret your results, including the p-value.
6.Based on your findings in 1-5, what is your opinion about using CREDIT BALANCE to predict INCOME? Explain.
7.Compute the 95% confidence interval for beta-1 (the population slope). Interpret this interval.
8.Using an interval, estimate the average income for customers that have credit balances of $4,000. Interpret this interval.
9.Using an interval, predict the income for a customer that has a credit balance of $4,000. Interpret this interval.
10.What can we say about the income for a customer that has a credit balance of $10,000? Explain your answer.
In an attempt to improve the model, we decide to do a multiple regression analysis predicting INCOME based on CREDIT BALANCE, SIZE and YEARS.
11.Using MINITAB run the multiple regression analysis using the variables CREDIT BALANCE, SIZE and YEARS to predict INCOME. State the equation for this multiple regression model.
12.Perform the Global Test for Utility (F-Test). Explain your conclusion.
13.Perform the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, which independent variables should we keep and which should be discarded. If appropriate, re-run the multiple regression using only the significant independent variables and the dependent variable. Include your output and interpret it.
14.Is this multiple regression model better than the linear model that we generated in parts 1-10? Explain.
15.All DeVry University policies are in effect, including the plagiarism policy.
16.Project Part C report is due by the end of Week 7.
17.Project Part C is worth 100 total points. See grading rubric below.
Summarize your results from 1-14
Data:
Location Income ($1000) Size Years Credit Balance($)
Urban 27 1 2 2631
Rural 25 4 2 2047
Suburban 25 1 1 3155
Suburban 26 1 2 3913
Rural 30 5 5 2660
Urban 29 1 3 3531
Rural 33 6 10 2766
Urban 30 1 4 3769
Suburban 32 2 4 4082
Urban 34 1 6 3806
Urban 35 1 8 4049
Urban 40 1 9 4073
Rural 30 6 9 2697
Rural 33 6 11 2914
Urban 42 2 10 4073
Suburban 32 2 4 4310
Urban 43 2 10 4199
Urban 43 2 10 4253
Rural 33 7 13 3104
Urban 47 2 10 4293
Subu rban 35 3 5 4456
Urban 54 2 11 4340
Suburban 42 3 5 4925
Rural 36 7 13 3178
Urban 57 3 11 4391
Suburban 44 3 6 4947
Rural 38 7 15 3203
Urban 54 3 8 4354
Urban 54 3 10 4366
Suburban 46 4 6 5003
Rural 40 7 15 3250
Urban 60 4 11 4402
Urban 58 4 10 4397
Urban 61 5 13 4595
Urban 61 5 13 4786
Urban 62 6 14 4888
Suburban 49 5 8 5148
Urban 68 6 14 5011
Suburban 57 6 8 5220
Rural 45 8 16 3257
Urban 71 7 15 5528
Suburban 57 7 9 5283
Suburban 64 8 9 5332
Rural 45 8 17 3304
Urban 74 7 19 5553
Suburban 65 8 10 5484
Rural 47 8 18 3342
Rural 53 8 18 3788
Suburban 66 8 10 5756
Suburban 69 8 10 5861
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]]>Mineral Mining Company sends one truckload of iron and copper ore daily from the mine to the processing plant. The truck has a weight capacity of 10 tons and a volume capacity of 1200 cubic feet. Each pound of iron ore takes up 0.04 cubic feet of space and yields a net profit of $0.30 when processed. Each pound of copper ore uses 0.08 cubic feet of space and provides $0.50 of net profit. The following LP model is proposed, where I is the number of pounds of iron ore to load on the truck and C is number of pounds of copper ore to load on the truck: Maximize 0.3 I + 0.5 C Subject to I + C < 20000 0.04 I + 0.08 C < 1200 I , C > 0 a. Solve the problem graphically. Explain the optimal solution and objective function value in the context of the problem. b. Graphically and algebraically determine the sensitivity range of each objective function coefficient at the optimal solution of the linear program in Problem 5. Explain the meaning of each range in the context of the problem. c.For each constraint that holds with equality at the optimal solution of the linear program in the given problem, perform the following: – Graphically and algebraically determine the sensitivity range of the right-hand-side value. – Calculate the shadow price associated with each sensitivity range found in part (a). Explain the meaning of the shadow price in the context of the problem. For the problem of Mineral Mining Company in Problem 5, management is considering leasing one of the following two new trucks to replace the existing one: TRUCK WEIGHT VOLUME ADDITIONAL TYPE CAPACITY(lb) CAPACITY (ft)3 COST ($/day) Tr 22/12 22,000 1,200 100 Tr 20/13 20,000 1,300 150 Should the company replace the old truck? And, if so, with which one of the new trucks should the company replace? Explain. (Use results from the last problem)
1. Mineral Mining Company sends one truckload of iron and copper ore daily from the mine to the processing plant. The truck has a weight capacity of 10 tons and a volume capacity of 1200 cubic feet. Each pound of iron ore takes up 0.04 cubic feet of space and yields a net profit of $0.30 when processed. Each pound of copper ore uses 0.08 cubic feet of space and provides $0.50 of net profit. The following LP model is proposed, where I is the number of pounds of iron ore to load on the truck and C is number of pounds of copper ore to load on the truck:
Maximize 0.3 I + 0.5 C
Subject to
I + C 0
Solve the problem graphically. Explain the optimal solution and objective function value in the context of the problem. (7 points)
b. Graphically and algebraically determine the sensitivity range of each objective function coefficient at the optimal solution of the linear program in Problem 5. Explain the meaning of each range in the context of the problem. (6 points)
For each constraint that holds with equality at the optimal solution of the linear program in Problem 1, perform the following:
c. Graphically and algebraically determine the sensitivity range of the right-hand-side value. (4 points)
d. Calculate the shadow price associated with each sensitivity range found in part (c). Explain the meaning of the shadow price in the context of the problem. (6 points)
e. For the problem of Mineral Mining Company in Problem 1, management is considering leasing one of the following two new trucks to replace the existing one:
Truck Type
Weight Capacity (lb)
Volume Capacity (ft)^3
Additional Cost ($/day)
Tr 22/12
22000
1200
100
Tr 20/13
20000
1300
150
Should the company replace the old truck? And, if so, with which one of the new trucks should the company replace? Explain. (Use results from problem c and d) (5 points)
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]]>1.Oak Construction Company built 128 houses in Hilltop Estates. If the company built 7 times as many colonial style houses as ranch style houses, how many ranch style houses were erected?
14 |
21 |
16 |
24 |
2.Calculate the weighted mean for the following data: value=10, weight=2; value=12, weight=6; value=15, weight=8; value=18, weight=6; value=20, weight=2
36 |
4.8 |
24 |
3.This year Bronson’s Tire Co. reported assets of $545,350 which is $120,640 more than last year. If owner’s equity was $192,500 last year, what was the amount of liabilities reported on last year’s balance sheet?
$232,210 |
$473,490 |
$352,850 |
$427,930 |
4. Laser Printing and Graphics offers cash discounts of 2/15, 1/20, n/30 to customers on all purchases. A customer purchased $18,000 of merchandise on May 20. What is the amount of the net payment if the invoice was paid on June 8?
$17,640 |
$18,000 |
$17,820 |
$16,200 |
5.Matt Stinson invested $4,000 in a simple interest account paying 5.5% per year. If he received $385 in interest, how long did he leave the money in the investment? (Express your answer to the nearest hundredth of a year.)
21 months |
1.5 years |
21 weeks |
175 days |
6.Junko Kiera borrowed $13,000 at a discount loan rate of 12% for 30 months. Determine the true interest rate of Junko’s loan.
0.171 |
0.152 |
0.133 |
0.141 |
7.Klemson High-Tech Industries borrowed $65,000 for three years at 14% compounded semi-annually. How much interest will they pay on the loan when they pay it off at the end of the term of the loan? (Express your answer to the nearest cent.)
$32,547.52 |
$14,627.80 |
$9,100.00 |
$32,306.73 |
8.Determine the future value of an ordinary annuity paying 10% quarterly for nine years if quarterly deposits of $450 are made throughout the nine years.
$25,785.64 |
$29,830.08 |
$4,479.53 |
$6,813.19 |
9.An asset was purchased on January 3rd costing $75,000 with a salvage value of $2,800 and an estimated useful life of five years. Find the depreciation expense using the straight-line method.
$15,000 |
$15,440 |
$14,440 |
$13,750 |
10.Mahalyk’s Water Fun Shoppe specializes in jet skis. Mahalyk’s inventory records showed the following for the past year: purchased 30 jetskis on February 10th at a cost of $4,000 per jetski; purchased 100 jetskis on May 12th at a cost of $3,000 per jetski; purchased 20 jetskis on June 15th at a cost of $3,500 per jetski; purchased 50 jetskis on July 20th at a cost of $2,500 per jetski Use the Average Cost Method to determine Mahalyk’s value of ending inventory at the end of July if they had 75 jetskis left in inventory.
$230,625 |
$210,000 |
$255,000 |
$187,500 |
1. Which of the following statements is TRUE?
There is some loss of information when raw data is tallied into a stem-and-leaf display. |
For a stem-and-leaf display, the leaf for the value 98 is 9. |
The stem in a stem-and-leaf display is the leading digit. |
For a stem-and-leaf display, the stem for the value 67 is 7. |
2.Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. The weighted mean hourly wage is:
$9. |
$9.67. |
$10.67. |
$11. |
3.According to which classification or type of probability are the events equally likely?
Classical |
Relative frequency |
Subjective |
Mutually exclusive |
4.A study determines that 60% of the voters in a town intend to vote for the incumbent mayor. If a sample of 8 people is selected, using the binomial formula, what is the approximate probability that 6 of the 8 people surveyed intend to vote for the incumbent?
0.47 |
1.28 |
0.6 |
0.21 |
5.What is a listing of all possible outcomes of an experiment and their corresponding probability of occurrence called?
Random variable |
Probability distribution |
Subjective probability |
Frequency distribution |
6.What kind of distributions are the binomial and Poisson distributions?
Discrete |
Continuous |
Both discrete and continuous |
Neither discrete or continuous |
7.Which of the following is NOT true regarding the normal distribution?
Mean, median and mode are all equal. |
It has a single peak. |
It is symmetrical. |
The points of the curve meet the X-axis at z = 3 and z = 3. |
8.The mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100. What is the z-score for an income of $1,100?
1.00 |
2.00 |
1.683 |
-0.90 |
9.Which of the following is NOT a component of the decision-making process?
Alternatives |
Payoff |
States of nature |
Seasonal indexes |
10.Applying probabilities to a payoff table results in:
expected opportunity loss. |
expected monetary value. |
expected value of perfect information. |
decision tree. |
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