excel and statistical econ problems

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Econ E270 Introduction to Statistical Theory in Economics and Business

Fall 2015

Homework 1 Due Date: Sept. 16, in class

• Name : ________________________________________________

• Signature : ________________________________________________

• Date : ________________________________________________

• Instructions:

1. Write your assigned student number in the box.

2. Submit the assignment with the pages stapled together.

3. To receive full credit, answers must be accompanied with relevant solutions/explanations.

4. Write your response in the relevant space provided. Responses provided elsewhere will be ignored. Furthermore, responses with unintelligible handwriting will be treated as incorrect.

5. You acknowledge that this is your own individual work. Late homework is not accepted.

Student Number

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1. Mary is the proprietor of a flower shop in a local town. She is interested in gauging the dollar-amount distribution of orders she receives for special events. The Excel file “hw1 mary flower shop” contains 50 randomly selected orders, to the nearest dollar, she collected based from sales receipts.

1) According to our guide for determining the number of classes, how many classes are

there?

2) What is the class width?

3) Using Excel, prepare the frequency distribution, showing columns for the (i) frequency, (ii) percent frequency, and (iii) cumulative frequency. Print the Excel output and staple to the back of the homework.

4) Using Excel, prepare the histogram, using the percent frequency. Label the axes and provide the title “Mary’s Flower Shop Orders.” Print the Excel output and staple to the back of the homework.

5) Would we expect the mean orders to be greater than or less than the median? Explain using the shape of the histogram revealed by the data.

6) Should Mary gauge her sample of average orders using the mean or the median? Explain.

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2. Anderson, page 120, question 13. In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. City: 16.2 16.7 15.9 14.4 13.2 15.3 16.8 16.0 16.1 15.3 15.2 15.3 16.2

Highway: 19.4 20.6 18.3 18.6 19.2 17.4 17.2 18.6 19.0 21.1 19.4 18.5 18.7

1) Calculate the mean, median, and mode for city driving. (You may use Excel for this,

writing down the answers below.)

2) Calculate the mean, median, and mode for highway driving. (You may use Excel for this, writing down the answers below.)

3) Use the mean, median, and mode to make a statement about the difference in performance for city and highway driving.

3. Anderson, page 121, question 19. Annual revenue for Corning Supplies grew by 5.5% in

2007, 1.1% in 2008, -3.5% in 2009, -1.1% in 2010, and 1.8% in 2011. What is the mean growth annual rate over this period? (You may use Excel for this, writing down the answers below.)

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4. Anderson, page 121, question 21. If an asset declines in value from $5,000 to $3,500 over nine years, what is the mean annual growth rate in the asset’s value over these nine years?

5. Suppose the time needed to assemble a particular gizmo has a bell-shaped distribution. The mean assembly time is 125 minutes and the standard deviation is 12 minutes.

1) What percentage of the gizmos are assembled between 101 and 149 minutes?

2) Between what two assembly times would approximately 68% of the values fall?

6. Suppose the average age of employees working in a community bank is 28 years with a standard deviation of 5 years. A histogram reveals that the distribution of ages is not bell- shaped (not normally distributed). Within what range of ages would at least 85% of the age of the workers fall?

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7. Suppose the assets of the ten largest banks in the world are arranged as follows.

Bank Assets ($ billions) 1 902 2 873 3 721 4 715 5 674 6 673 7 654 8 652 9 642 10 613

Determine the following: (You may use Excel for this, writing down the answers below.)

1) Interquartile range.

2) 20th percentile.

3) 60th percentile.

4) Are the bank assets interval or ratio data? Explain.