Statistics homework help

STAT 33001                         Biostatistics
Project – Outline
 
You are expected to complete a mini project related to descriptive and/or inferential statistics.
The project must contain the following components

  1. Title of the project
  2. Introduction and Objectives
  3. Data collection: Data should be a real a data set (you may find the data on the internet, in published papers, but please provide the source).
  4. Display the data graphically using
  5. Compute all relevant summary statistics. You may here use R or other software for the calculations.
  6. Perform the inferential statistics (Interval estimation/ hypothesis testing etc.) Include the test statistics that you are using. You may here use R or other software for the calculations. Statistics homework help.
  7. Conclusions
  8. References
  • The project should be typed using a
  • Use complete
  • The length of the project should be maximum 4
  • Work alone or in a group of up to 5 people. Please submit only one project for each group. Include the name of all group members on the project.

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 Study of Fuel Efficiency for Imported and Domestic Passenger Cars
When people go to shop for a new car one of the main criteria they look at is the fuel
efficiency of the car. Many people who use fuel efficiency to determine what car to purchase
lean toward foreign made cars claiming that they get more miles per gallon than American
made cars. This study attempts to use the data for the average miles per gallon for domestic
and imported vehicles over a 24 year period from 1990-2013 to determine whether fuel
efficiency should play a significant role in whether to purchase a foreign made car over an
American made car. Statistics homework help.
The following table lists the average fuel efficiency of domestic and imported vehicles
from 1990-2013 based on data from the U.S. Department of Transportation found at
www.rita.gov
Table 1
Fuel Efficiency for Passenger Cars (mpg)
Year Domestic Imported
1990 26.9 29.9
1991 27.3 30.1
1992 27.0 29.2
1993 27.8 29.6
1994 27.5 29.7
1995 27.7 30.3
1996 28.1 29.6
1997 27.8 30.1
1998 28.6 29.2
1999 28.0 29.0
2000 28.7 28.3
2001 28.7 29.0
2002 29.1 28.8
2003 29.1 29.9
2004 29.9 28.7
2005 30.5 29.9
2006 30.3 29.7
2007 30.6 32.2
2008 31.2 31.8
2009 32.1 33.8
2010 33.1 35.2
2011 32.7 33.7
2012 34.4 36.4
2013 35.5 37.1
28 30 32 34 36
Boxplot for Imported MPG
28 30 32 34
Boxplot for Domestic MPG
Five Number Summary for the fuel efficiency of a Domestic passenger car with the
corresponding boxplot
Table 2
Five Number Summary for the fuel efficiency of an
Imported passenger car with the corresponding
boxplot
Table 3
Line graph comparing the fuel efficiency of a domestic vehicle to an imported vehicle from
1990-2013
Domestic mpg
Minimum 26.90
1
st Quartile 27.80
Median 28.90
3
rd Quartile 30.75
Max 35.50
Mean 29.69
Imported mpg
Minimum 28.30
1
st Quartile 29.20
Median 29.90
3
rd Quartile 31.90
Max 37.10
Mean 30.88
Bar graph comparing the fuel efficiency of a domestic vehicle to an imported vehicle from 1990-
2013
Domestic Imported
2 8 3 0 3 2 3 4 3 6
Side-by-side box plot
>
Determine whether the fuel efficiency varies enough that it should play a role in whether to
purchase an American or foreign made car. Statistics homework help.
H0
: μimported=μdomestic
Ha
: μimported ≠ μdomestic
Using the two sample t-test we get the following test statistic
t
0=
x1−x2

s1
2
n1
+
s2
2
n2
=1.678
and critical value t
0.025=¿2.069.
A 95 percent confidence interval is given by
(-0.2377, 2.62104).
Since the test statistic is smaller than the critical value we fail to reject the null hypothesis.
Therefore fuel efficiency should not play a significant role in whether to purchase a foreign or
an American made vehicle.
References
United States, Bureau of Transportation Statistics, Department of Transportation. “Table 4-23:
Fuel Efficiency of U.S. Light Duty Vehicles”. Retrieved August 4, 2015, from:
http://www.rita.dot.gov/bts/sites/rita.dot.gov.bts/files/publications/
national_transportation_statistics/html/table_04_23.html. Statistics homework help.

 
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Breaking Even Assignment

Breaking Even Assignment
Unit VII Assignment: Breaking Even
 
Breakeven analysis uses two functions to describe the revenue and cost of a particular product. The breakeven point is the number of products that a business must produce and sell so that the money coming in is equal to the money going out. In this assignment, you will be asked to create a system of equations based on the cost and revenue of a particular business. You will solve the system to determine the business’s breakeven point.
 
Instructions: Imagine that you are business owner who produced a particular item to sell in your new store. Answer questions 1–10. Save all of your work to this template and submit it in Blackboard for grading.

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  1. Briefly explain one item that you will be producing and selling in your store.

 
 
 

  1. How much does the item cost you to produce? Consider the cost of materials and labor. Select an amount between $1 and $50. Round to the nearest dollar.

 

Cost per item produced = $

 

  1. How much will you sell the product for? Select an amount between $1 and $100. The sold price must be more than what it costs to produce the item. Round to the nearest dollar.

 

Price per unit sold = $

 

  1. Write the cost function, C(x), of producing x amount of items. Assume that you have a fixed cost $5,000. Replace the “?” with the appropriate numbers.Breaking Even Assignment

 
C(x) = fixed cost + (cost per item produced)(x)
C(x) = ? + (?)(x)
 

  1. Write the revenue function, R(x), from the sale of x items. Replace the “?” with the appropriate numbers.

 
R(x) = (price per item sold)(x)
R(x) = (?)(x)
 

  1. Replace C(x) and R(x) with y. This means that the cost and revenue will be the same. Write the system of equations below.

 
Y = write equation found for C(x)
Y = write equation found for R(x)
 
 

  1. Use the substitution method to solve the system of equations found in question 6. The solution is the breakeven point. Show each step of your work below. Round your final answer for x to the nearest whole number and use the rounded value of x to solve for y. Round y to the nearest cent or to two decimal places.

 
 
 
 
 
 

  1. How many items must you sell and produce in order to break even?

 
 
 
 
 
 

  1. What does break-even mean? In your own words, include what the x and y-coordinates of the break-even point mean in your definition. You should not restate the coordinates you found above.

 
 
 
 
 

  1. How many items will you need to sell in order to make a profit of $2,500? Round up to the nearest whole number.

 
First, find P(x). To do this, substitute the expressions for R(x) and C(x) found in questions 4 and 5 into the equation below and simplify.
 
P(x) = R(x) – C(x)
 
 
 
 
 
Next, replace P(x) with 2500 into the equation above and solve for x. Round up to the nearest whole number. Show your work below.
 
 
 
 
 
 
 
 
Answer: You need to sell ____ items in order to make a profit
 
Breaking Even Assignment

 
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Excel Assignment Paper

Excel Assignment Paper
Open the Excel data file in the Week 8 folder. Your spreadsheet should like this:
This week we will complete the calculation and explanation of descriptive statistics with the help of Excel. Below are the commands needed to compute the respective values.
Measures of Variability/Dispersion1:
Min.
Max.
Range
Variance
Standard Deviation Quartiles:
Q1: Q3:
=min(array of values) =max(array of values) =(Max-Min)
=VAR.P(array of values)2 =STDEV.P(array of values)
=QUARTILE.INC(array of values, 1)3 =QUARTILE.INC(array of values,3)
 
1 In order to calculate the Range in Excel, we need to calculate the High and Low value(s) in the data set(s).
2 In Excel, like all statistics programs, you have the option of calculating some measures for a “sample” or for a “population”. We are going to use the Population form. The alternative form of the function in Excel for variance and standard deviation would have “.S” instead of a “.P”. Excel Assignment Paper.
3 In Excel, there is the option to INClude the median the calculation of the quartiles or EXClude the median. Including, as we have done, will affect the Q1 and Q3 calculations and provide more symmetrical quartiles. The disadvantage to this is that it will make it more difficult to identify outliers. Thus, we assume more normality in our distribution.

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Assignment 2
IQR4:
McCormack CRIM.3950.01
Normality: Skewness:
Kurtosis:
=(Q1-Q3)
=SKEW.P(array of values)
=KURT(array of values)
The measures of skewness and kurtosis may be unfamiliar and/or new to you. These values can also be used to describe how normally distributed a set of data is. Each also has a threshold – or rule of thumb – value, which one can use to determine how normal (or not) a distribution is. Skewness measures the symmetry of the distribution. The closer the value is to 0 the more symmetrical the distribution is, e.g. the less skewed. The value measures the relative size of the two tails. Data that has skewness measured greater than | 1 | are highly skewed (positive or negative direction indicates the direction of the skew). Kurtosis measures the “peakedness” of the distribution. Excel calculates this value using the “minus 3” rule – a correction that actually reflects a normal distribution with a value of 0. Thus, in Excel, the closer the value is to 0, the more normally distributed the distribution is. Both values, like many of our descriptive measures, are heavily influenced by our sample size.
Like before, add these measures in the Excel spreadsheet. Begin below “mean”, in cell A49. Your spreadsheet should look like this (open your previous assignment if needed):
Using the commands above, let’s calculate the values. Ultimately, you should come up with the following values – formatted in tabular form:
4 The Interquartile Range (IQR) describes where the middle 50% of the data is located.
Assignment 2
McCormack CRIM.3950.01
All Reported Crimes
Annual Number in Boston 1985-2014
Mode N/A (multimodal) Median 35,788 Mean 43,069 Min. 22,018 Max. 70,003 Range 47,985 Variance 258,567,142.6
Standard Deviation Q1
Q3
IQR
Skewness Kurtosis
16,080.02 31,718.75 56,188 24,452.25 0.47 -1.27
How would we explain these results? First, we see a fairly large range. Annually, we have seen a near consistent decrease in the overall number of reported crime in Boston. Its peak was in 1989, with just over 70,000 crimes reported, and a low in 2014, with just over 22,000 crimes reported. With a large range usually comes a large standard deviation. A value of just over 16,000 indicates that the typical distance each annual total is away from the mean is about 16,000. So, the annual values tend to differ. We know the IQR represents where the middle 50% of the data lie, so half of all years had between about 31,000 and 56,000 reported crimes. Excel Assignment Paper.
Variability and Dispersion
Calculate the measures of variability and dispersion for the same 3 offenses you have worked with previously. Create a similar table for those same 3 offenses.
Copy/paste them into or create in a Word document (.doc or .docx) which will be submitted.
Beneath each table (3 you picked and created), write a 100-word paragraph describing the measures of variability and dispersion.
Ensure all of your tables and write-ups are submitted in one Word (.doc or .docx) file for Assignment 3.
Worked Example for Week 10
Using the same data from our previous Worked Examples, along with new data, I will show you how you can test the difference between means using some basic descriptive statistics of the two samples being compared. As a result, you will see an example of hypothesis testing: a statistical test that examines the possible significant difference between two groups. The process can be done for proportions as well, but for our purposes we will focus on means.
To perform this test we will require descriptive statistics for two groups. The first group will be the sample of prisoners we have used in all of our Worked Examples. The second group will be a new hypothetical group from a different prison. Let’s assume the first group is male prisoners and the second group is female prisoners. Thus, we are testing to see if there is a significant difference in the mean number of months incarcerated for males and females.
Our null hypothesis is always written that the two means are equal. To reject this, we need to find a significant difference. Similar to “innocent until proven guilty”, we assume equal means until proven different. The null hypothesis can be written as follows:
H0: μ1=μ2 or 1=2
Our alternative hypothesis is written that the two means are not equal (significantly different). Excel Assignment Paper.
H1: μ1≠μ2 or 1≠2
Notice the subscript numbers next to the symbols for means: this is simply referring to each group. Each symbol with a “1” subscript requires the descriptive data from Group 1 and each symbol with a “2” subscript requires the descriptive data from Group 2. It does not necessarily matter which group you refer to as “1” and “2”; what is important is that you are consistent throughout the hypothesis test processes*. If you mix the groups throughout the steps, you will end up with incorrect and invalid results. Now that we have stated our hypothesis, we must list the descriptive statistics needed for the hypothesis test.
Group 1, as we stated, is the male prisoners. Since we have used this data throughout our Worked Examples, we already have all the information needed.

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N1 = 10 1 = 4 s12= 3.4
Recall N is our sample size. is the mean. S2 is the variance. This is very important; the standard deviation is not required in this test, we need to use the variance (standard deviation “squared”).
Group 2, as we stated, is the female prisoners. For our purposes, I will simply supply the descriptive statistics needed for the hypothesis test.
N2 = 12 2 = 2 s22= 2
Now that we have the required information we can begin to test the hypothesis that the mean number of months incarcerated is equal between male and female prisoners. From our two small samples we see that males have an average of 4 months and females have an average of 2 months. Remember, these are very small samples so we must use that information in combination with the variability to determine if we have enough information to conclude the difference is significant.
Step 1: Compute the standard error.
This step is tedious and requires a lot of information.
S1- 2=√(N1 )(N1 )S1- 2=√( )( ) N1 N1
S1- 2=.73
Step 2: Compute the test statistic (t-value). We simply subtract the mean of group 2 from the mean of group 1 and divide by the standard error, the value we just calculated. Excel Assignment Paper.
T= T= T= 2.74
Step 3: Determine the critical value. This step requires knowledge of what alpha level you will be using and a T-distribution table of values. As is common in criminal justice research we will look at alpha levels of .05 and .01.
The critical value for our hypothesis test with an alpha level of .05 is 2.086 The critical value for our hypothesis test with an alpha level of .01 is 2.845 Step 4: Compare test statistic (t-value) and critical value. Interpret.
We computed a test statistic of 2.74 which is larger than the first critical value of 2.086; we reject the null hypothesis that the mean number of months incarcerated is equal between males and females. We are stating that based on the information provided to us we can say at the .05 alpha level (or with 95% confidence) the means are different.
When examining the test statistic of 2.74 at the .01 alpha level we fail to reject the null hypothesis that the mean number of months incarcerated is equal between males and females. This is due to the test statistic being lower than the critical value of 2.845. We are stating that based on the information provided to us we can’t say at the .01 alpha level the means are
different. Essentially, we can be 95% confident that the observed difference is true or not due to sampling error/chance but we cannot be 99% confident.
*As a note, depending on the values of the means and the order in which you subtract one from the other you may end up with a negative test statistic (t-value). That is fine. When this happens simply compare the numerical value itself to the critical value just as you would if the value was positive. The negative only implies directionality, a component we are not focusing on. The interpretation of actual difference is what is important. Excel Assignment Paper.
 

 
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5-3 Assignment: Means: Test Of Hypothesis

5-3 Assignment: Means: Test Of Hypothesis
Scenario
You have been hired by the Regional Real Estate Company to help them analyze real estate data. One of the company’s Pacific region salespeople just returned to the office with a newly designed advertisement. It states that the average cost per square foot of his home sales is above the average cost per square foot in the Pacific region. He wants you to make sure he can make that statement before approving the use of the advertisement. The average cost per square foot of his home sales is $275. In order to test his claim, you collect a sample of 1,001 home sales for the Pacific region. 5-3 Assignment: Means: Test Of Hypothesis.
Prompt
Design a hypothesis test and interpret the results using significance level α = .05.
Use the House Listing Price by Region document to help support your work on this assignment. You may also use the Descriptive Statistics in Excel and Creating Histograms in Excel tutorials for support.
Specifically, you must address the following rubric criteria, using the Module Five Assignment Template.
Setup: Define your population parameter, including hypothesis statements, and specify the appropriate test.
Define your population parameter.
Write the null and alternative hypotheses. Note: Remember, the salesperson believes that his sales are higher.
Specify the name of the test you will use.
Identify whether it is a left-tailed, right-tailed, or two-tailed test.
Identify your significance level.
Data Analysis Preparations: Describe sample summary statistics, provide a histogram and summary, check assumptions, and find the test statistic and significance level.
Provide the descriptive statistics (sample size, mean, median, and standard deviation).

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Provide a histogram of your sample.
Describe your sample by writing a sentence describing the shape, center, and spread of your sample.
Determine whether the conditions to perform your identified test have been met.
Calculations: Calculate the p value, describe the p value and test statistic in regard to the normal curve graph, discuss how the p value relates to the significance level, and compare the p value to the significance level to reject or fail to reject the null hypothesis.
Determine the appropriate test statistic, then calculate the test statistic.
Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean (Pacific), and the target is 275. 5-3 Assignment: Means: Test Of Hypothesis.
Calculate the p value.
Note: For right-tailed, use the T.DIST.RT function in Excel, left-tailed is the T.DIST function, and two-tailed is the T.DIST.2T function. The degree of freedom is calculated by subtracting 1 from your sample size.
Choose your test from the following:
=T.DIST.RT([test statistic], [degree of freedom])
=T.DIST([test statistic], [degree of freedom], 1)
=T.DIST.2T([test statistic], [degree of freedom])
Using the normal curve graph as a reference, describe where the p value and test statistic would be placed.
Test Decision: Discuss the relationship between the p value and the significance level, including a comparison between the two, and decide to reject or fail to reject the null hypothesis.
Discuss how the p value relates to the significance level.
Compare the p value and significance level, and make a decision to reject or fail to reject the null hypothesis.
Conclusion: Discuss how your test relates to the hypothesis and discuss the statistical significance.
Explain in one paragraph how your test decision relates to your hypothesis and whether your conclusions are statistically significant. 5-3 Assignment: Means: Test Of Hypothesis.

 
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