An expert who works for a car magazine obtained random data (rounded to the nearest thousand) among two categories of used or new cars: Domestic Foreign

The expert would like to understand sales based on list price (rounded to the nearest thousand dollars), sale price (rounded to the nearest thousand dollars), and number of days it takes to sell each car. The complete data set is in the file named Cars.

Managerial Report

Prepare a report (see below) that summarizes your assessment of the nature of the car market. Be sure to include the following seven items in your report.

1. Calculate descriptive statistics (mean, median, range, standard deviation, and coefficient of variation) to summarize each of the three variables for the all Domestic cars.
   • Use z-scores to determine if there any outliers in the data set for any of the three variables. If there are any outliers in any category, please list them and state for which category they are an outlier.
   • If a result is an outlier, state whether it is below or above the mean.
   • How can one use the above descriptive statistics to understand the Domestic car market better?
   • Could there be any other descriptive statistics that can help one understand the Domestic car market better?
2. Descriptive statistics (mean, median, range, standard deviation, and coefficient of variation) to summarize each of the three variables for the all Foreign cars.
   • Use z-scores to determine if there any outliers in the data set for any of the three variables.
   • If there are any outliers in any category, please list them and state for which category they are an outlier.
   • If a result is an outlier, state whether it is below or above the mean.
   • How can one use the above descriptive statistics to understand the Foreign car market better?
   • Could there be any other descriptive statistic that can help one understand the Foreign car market better?
3. Compare your summary results from #1 and #2. Discuss any specific statistical results that would help the car expert understand the two-car markets.
4. Develop a 98% confidence interval estimate of the population mean sales price and population mean number of days to sell for Domestic cars. What is the margin of error?
   • Interpret what each confidence intervals means. How can both confidence intervals provide useful car sales information?
   • What other confidence interval would you choose to compute to obtain more information related to Domestic car sales? Explain why.
   • What happens to the confidence interval as the level of confidence is increased?
5. Develop a 98% confidence interval estimate of the population mean sales price and population mean number of days to sell for Foreign cars. What is the margin of error?
   • Interpret what each confidence intervals means. How can both confidence intervals provide useful car sales information?
   • What other confidence interval would you choose to compute to obtain more information related to Domestic car sales? Explain why.
6. Assume the car expert requested estimates of the mean number of days to sell for the Domestic cars with a margin of error of seven days and the mean selling price of foreign cars with a margin of error of eight days.
   • Using 98% confidence, how large should the sample sizes be for each one?
   • How could the sample size formula be useful in understanding both types of car businesses? What are some advantages of a larger sample size?
   • Suppose a Domestic car has a list price of $30,000 and a Foreign car has a list price of $30,000. What is your estimate of the final selling price (based on the percent difference for the sale and list price) and number of days required to sell each of these cars?
   • How would these two estimates be useful in this application?

Write a report that adheres to the formatting and APA expectations outlined on the Citing & APA Resources page (Links to an external site.) in the CSU-Global Writing Center. As with all written assignments at CSU-Global, you should have in-text citations and a reference page.

Submit your Excel file in addition to your report.

Requirements:

1. Paper must be written in third person.
2. Your paper should be four to five pages in length

THIS IS A STATISTICS COURSE.

Please respond to two peers.

200 word per peer

Remember this is NOT a Paper, but a Discussion Post. Each peer will have different question to answer.

Please watch video.

TURNITIN Score must be below 12%

APA In Text Citation Please.

Watch the video, then read below.

https://mediaplayer.pearsoncmg.com/assets/_jGvVe5Jbkm44I2D0TWEMnsz6A6Y7fin

This video explains the normal distribution via the binomial distribution: The distribution of the number of heads thrown on 20 coins approximates the normal. This is used to explain that the normal distribution is the mathematical consequence of adding up a large number of random events. Some examples are given of normal distributions in the natural world (mass of ants) and social world (age of marathon runners) and explained in terms of these phenomena resulting from the aggregation of random events.

Respond to peer one regarding: Do natural phenomena such as hemoglobin levels or the weight of ants really follow a normal distribution? If you add up a large number of random events, you get a normal distribution.

Peer One: Ebenezer Tetteh-Ahinakwa post below

Do natural phenomena such as hemoglobin levels or the weight of ants really follow a normal distribution? If you add up a large number of random events, you get a normal distribution.

Most natural phenomena follow a normal distribution. This is because natural phenomena is influenced by many factors, for example, height can be influenced by genes, environmental factors, sex, among others. And as Bennett, Briggs, and Triola (2014) state, any quantity that is influenced by many factors is likely to follow a normal distribution.

Also, for most natural phenomena data sets the data values are clustered near the mean, giving the distribution a nearly normal peak, and they are also spread evenly around the mean making the distribution symmetric. This means that large deviations from the mean become increasingly rare producing the tapering tails for the distribution (Bennett, Briggs, & Triola, 2014).

There is also the aspect of the Central Limit Theorem which shows that the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. As we have seen, natural phenomena tends to be influenced by a sufficiently large number of independent random variables, each with finite mean and variance. As a result, the occurring data sets from these independent random variables will be normally distributed. However, it is important to remember that no data set can ever perfectly match a theoretical distribution. This is because a data set will sometimes deviate or become skewed making it unable to be a perfect match for a theoretical distribution.

References

Bennett, J., Briggs, W. & Triola, M. (2014). Statistical reasoning for everyday life (4th ed.). Boston, MA: Pearson Education, Inc.

RESPOND to peer two Kyasha Ware regarding: How large a number makes a normal distribution?

How large a number makes a normal distribution?

When it comes to the normal distribution it is the most common and useful distribution to use in statistics in the central limit theorem. Also, known as the bell curve, the normal distribution has a symmetrical shape in which both sides are fifty percent even. This happens because the highest peak will decrease on both sides to create a format. In normal distributions, you can develop your mean, median, mode, standard deviation, and the empirical rule or also known as 68-95-99.7. All of these value results will show you where the height and width is to contrast the rest of the sample question. I personally feel like you can have a normal distribution curve of five to ten data values for standard deviation with a larger number. When it comes to subjects like heights, test scores, house values, and sugar levels normal distribution is the best way to get the averages whether they are low or high.

END of both Peer Post

The research firm LL Research collected data from 200 client businesses. They want to determine how the businesses compare among four variables:

2015 Profit in millions of dollars
2016 Profit in millions of dollars
2015-2016 Two-Year Change in Daily Average Customer Visits

Two-Year Average Number of Employees

Data collected for the sample of 200 businesses is contained in the file named Businesses, linked at the bottom of the page. Be sure to use all 200 data points.

Managerial Report
Prepare a report (see below) using the numerical methods of descriptive statistics presented in this module to learn how each of the variables contributes to the success of a client’s business. Be sure to include the following three items in your report.

1. Compute descriptive sample statistics (mean, median, two quartiles Q1 and Q3 (using QUARTILE.EXC), minimum, maximum, range, interquartile range, sample standard deviation, and coefficient of variation) for each of the four variables along with an explanation of what the descriptive statistics tell us about the client businesses.

• In this case, which measure of central tendency would be best for this application? Explain why.
• Which measure of variation would be best for this application? Explain why.
• How can one use the above descriptive statistics to understand the businesses better?
• Which graphical displays of data would you use to help understand or complement the above descriptive statistics? Explain how and why.

Note: QUARTILE.EXC works only for Excel 2010 or newer.

1. Compute the percent change in profit from 2015 to 2016 for each business.

• What would the percent change tell us in this application?
• Then use the z-score to determine which businesses were outliers with respect to percent change in profit.
• How would identifying outliers be useful in this application?
• What advice might you give to businesses that are outliers?
• How else would you determine outliers?

1. Compute the sample correlation coefficient, showing the relationship between percent change in profit and each of the other two variables (2015-2016 Two-Year Change in Daily Average Customer Visits and Two-Year Average Number of Employees).

• Explain what the correlation coefficients tell us about the three pairs of relationships. Use tables, charts, or graphs to support your conclusions.

APA format- you should have in-text citations and a reference page.

Submit your Excel file in addition to your report.

Requirements:

1. The paper must be written in third person.
2. Your paper should be four to five pages in length (counting the title page and references page) and cite and integrate at least one credible outside source.
3. Include a title page, introduction, body, conclusion, and a reference page.
4. The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.
5. The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure the Word document is in paragraph format, not numbered answers like a homework assignment.
6. The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs. Your conclusion should emanate (be aligned with) your findings.
7. Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignments

Provide CLEAR images of handwritten work (or in word if you prefer, as long as it is clear) for the for the following examples:

• Answer Questions #1 – 8. You do not need to show your work.
• #1) Find the expected value for the probability model shown below.
• Value $2 $4 $8 $30Probability 0.25 0.5 0.17 0.08
• #2) Find the missing value (???) in the probability model shown below.
• Value $2 $5 $8 $11Probability 0.18 0.33 ??? 0.28
• #3) In the probability model given below, the expected value is – $1.55. Find the missing value, x.
• Value $4 -$5 x -$8
• Probability 0.20 0.45 0.15 0.20
• #4) A large number of people were polled and asked which of four different animals were their favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you decide to carry out a simulation given these percentages. You decide to select two digits at a time. Which would be a proper assignment of digits for these teams?
• a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtleb) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtlec) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtled) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtlee) None of These
• #5) The expected value for the following scenario is $1.60. Write two different equations that give both a simplified equation using the expected value and a simplified equation for the total of all probabilities in the probability model.
• Value $3 -$4 $17Probability x y 0.08
• #6) Suppose that there are 513 students who are currently enrolled in AP Calculus and that we are looking for five randomly selected students to survey about their experiences in AP Calculus. The digit combinations 001-513 are assigned to represent the 513 students currently enrolled in AP Calculus. Using the random digits below, what are the numbers of the five students that will be selected for the survey? 71548 15233 53946 68713 72468 27601 13703 88692
• Student 1 = #_____, Student 2 = #_____, Student 3 = #_____, Student 4 = #_____, Student 5 = #_____
• #7) If you buy a ticket in a certain lottery game, 30% of the players will get paid $1, 20% of the players will get paid $6, and 5% of the players will get paid $55. All other players get paid nothing. What is the expected amount that a player of this lottery game will get paid?
• #8) In a certain card game you draw one card off a standard deck of 52 cards. If you draw a spade you get paid $12, if you draw a red Ace you get paid $20, and if you draw a red Queen you get paid $38. If you draw anything else, you get paid nothing. What should this game cost if it is to be a fair game? Use fractions in your work and then calculate the answer as a decimal rounded to 4 decimal places.

There are numerous variables that are believed to be predictors of housing prices, including living area (square feet), number of bedrooms, and number of bathrooms.The data in the Case Study No. 2.xlsx file pertains to a random sample of houses located in a particular geographic area.

• Develop the following simple linear regression models to predict the sale price of a house based upon a 90% level of confidence.Write the regression equation for each model.
  • Sale price based upon square feet of living area.
  • Sale price based upon number of bedrooms.
  • Sale price based upon number of bathrooms.
• Develop the following multiple linear regression models to predict the sale price of a house based upon a 90% level of confidence.Write the regression equation for each model.
  • Sale price based upon square feet of living area and number of bedrooms.
  • Sale price based upon square feet of living area and number of bathrooms.
  • Sale price based upon number of bedrooms and number of bathrooms.
  • Sale price based upon square feet of living area, number of bedrooms, and number of bathrooms.
• Discuss the joint statistical significance of each of the preceding simple and multiple linear regression models at a 90% level of confidence and 95% level of confidence.
• Discuss the individual statistical significance of the coefficient for each independent variable for each of the preceding simple and multiple linear regression models at a 90% level of confidence and 95% level of confidence.
• Compare any of the preceding simple and multiple linear regression models that were found to be jointly and individually statistically significant at a 90% level of confidence and select the preferred regression model. Explain your selection using the appropriate regression statistics.
• Interpret the coefficient for each independent variable (or variables) associated with your selected preferred regression model.
• Using the preferred regression model, predict the sale price of a house with the following values for the independent variables: 3,000 square feet of living area, 3 bedrooms, and 2.5 bathrooms.(Hint: You should only use the values for those independent variables that are specifically associated with your selected preferred regression model.)

Prepare a single Microsoft Excel file using a separate worksheet for each question

You will be expected to:

• perform certain calculations discussed in the assigned reading in order to derive an answer for each problem.
• use Microsoft Excel to complete each problem and submit a single Excel spreadsheet that contains a separate worksheet (i.e., separate tab) for each problem.
• have each worksheet be clearly labeled to identify the associated problem.to show all calculations or other work performed to derive your answer(s) for each problem.
• have your spreadsheet be fully functional (i.e., configured to allow the reader to not only see all numerical values but also be able to see the underlying formula associated with each calculated value).
• to label your work in each worksheet to clearly identify the nature of each piece of data or calculated value.