**Directions: Follow the directions below and use the Excel file attached to this assignment link. both a MS Word document for the Managerial Report and an Excel file showing your work.(Please use this template for your managerial report. Please note that this report must be submitted with an Excel spreadsheet showing your work.)**

After the Volkswagen “Dieselgate” in which VW admitted to circumventing the emissions control system in about 550,000 vehicles sold in the U.S. (Bartlett, Naranjo, & Plungis, 2017), regulatory agencies began testing the mileage claims of other automotive manufacturers.

What follows is a fictional scenario.

WX automotive manufactures cars for the global market. WX automotive claims that one of its diesel vehicles, the X-class, get 40 miles per gallon.

The Nation of Kimtopia is an importer of WX cars. Because of its limited budget, it has looked to UIW, namely, the Business Statistics class, to provide some statistical knowledge in order to assess the mileage claims of WX automotive. The Kimtopia Environmental Protection Agency has provided mileage data for a sample of 30 WX X-class cars and would like to assess whether or not the claims of WX can be trusted.

__Managerial Report__

You are to prepare a managerial report summarizing the results of your data analysis (details listed below) given the above scenario. This document should be professionally written, that is, the findings and their interpretations should be discussed in narrative form with complete sentences, using proper grammar and be free of writing errors (e.g., spelling, punctuation, etc). Statistical findings will be displayed in graphical and numerical formats, but the interpretations must be in narrative form. This report is to be prepared using MS Word along with a Excel spreadsheet showing your work.

1. Calculate the following descriptive statistics for the data: sample mean, sample standard deviation, range, median, first quartile and third quartile.

2. Using Excel’s Pivot Chart function, prepare a frequency histogram of the mileage data using a interval size of 2.

3. Develop a 95% confidence interval estimate of the population mean. Along with the actual confidence interval, make sure to specify the amount of your standard error and margin of error.

4. Interpret the interval you found in #3 above (that is, explain it in words).

5. Write out in narrative form and in statistical format your null and alternate hypotheses.

6. Test your hypotheses at a .05 significance level (i.e., 95% confidence level). Make sure to show your work.

7. What do your findings in #6 above tell you about your hypotheses (reject the null or do not reject the null)?

8. Write out in narrative form your interpretation of the indicated results in #7 above. Based on your results can WX’s mileage claim for the X-class be trusted?

9. Suppose now you find historical mileage data on the X-class that shows the population standard deviation to be 4.1 miles per gallon. What sample size would be needed to increase the finding’s accuracy to a .5 miles per gallon margin of error?

**10.**Draw the normal curve that depicts your hypotheses findings. Make sure to label the population mean (m), the alpha (a), the p-value, and the reject and do not reject zones. You can do this by hand and then insert a picture into your document or just upload a separate picture file to the assignment link.

Reference:

Bartlett, J. S., Naranjo, M., & Plungis, J. (October 23, 2017). An FAQ with everything you need to know about the VW ‘Dieselgate’. Retrieved from https://www.consumerreports.org/cro/cars/guide-to-the-volkswagen-dieselgate-emissions-recall-.