1. Assume that the starting salaries for the Class of 2013 college graduates is (rounded, in $1000’s) normally distributed with µ = 45 and σ = 5. (Based on real data.) a. Sketch and label the normal curve. b. In what range must a starting salary be for a graduate to be in (approximately) the highest 16% ? c. In what range must a starting salary be for a graduate to be in (approximately) the lowest .15% ? d. In what range must a starting salary be for a graduate to be in (approximately) the middle 95% ? e. What is the z-score for a graduate who has a starting salary of $42.5? f. What % of 2013 graduates are making less than $42.5?

Review the concepts of confidence interval and margin of error studied in this unit. Say you were researching some aspect of a population, and the sample proportion is 25% with a margin of error of 4% at the 95% confidence level. Does this mean that there is 95% chance that the population proportion is between 21% and 29%? Why or why not, and what might be the implications for your research in either case?

How does one decide upon the size of a sample?  Upon what does this decision depend?

A set of data is normally distributed with a mean of 37 and a standard deviation of 1.5. If you randomly select a data point and it is 37.75, which of the following would describe that data point?

• Unusually large (Statistically significant)
• Unusually small (Statistically significant)
• Not unusual (Not statistically significant)
• Not enough information

VII. You suggest a mean comparison procedure to evaluate differences between means of the drug groups and show her the following output.

drug emmean   SE df lower.CL upper.CL .group

1      79.9 1.59 16     76.5     83.2 A   

2      85.8 1.67 16     82.2     89.3   B  

3      88.9 1.98 16     84.7     93.1   B  

Results are averaged over the levels of: diet

Confidence level used: 0.95

P value adjustment: tukey method for comparing a family of 3 estimates

significance level used: alpha = 0.05

a. Explain to her that the SE's (standard errors) are a function of three factors in the model used.

b. How do you interpret the confidence limits of drug 2.

c. If this were your thesis project data, write a sentence explaining differences among the drug group means in the manner that you would in your thesis.

d. Do you have any suggestions for further analysis

The Mean Corporation would like to invest in the booming health food industry. It is considering the creation of a health-drink franchise called Goose Juice. The investment department of the Mean Corporation wants to investigate the feasibility of this venture by examining the profits of similar franchises. It believes that the venture will be feasible if an average annual profit of more than $89,000 can be expected from each Goose Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $8,200.

The Mean Corporation's statisticians would like to construct a hypothesis test for the mean annual profit (μ) earned by health-drink franchises. A random sample of 70 franchises were chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $90,250. The hypotheses that will be used by the statisticians are H₀: μ = 89,000 and H_a: μ > 89,000.

A.) Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer to 3 decimal places.

Z =

B.) Using the test statistic for the Mean Corporation's hypothesis test and level α = 0.05, the Mean Corporation should (accept, reject, not reject) the null hypthesis.

C.) If the sample size is increased to 170 (but the sample mean remains unchanged), the Mean Corporation should (accept, reject, not reject) the null hypothesis.

For problem 14.72 assume that the first seven homes are in Norfolk and the next eight are in Virginia Beach. After adding this variable by hand to the model as a dummy variable: 1 for Norfolk and 0 for VA Bch.

1. Assess multicollinearity for the model.

2. Interpret the coefficient for the dummy variable.

3. Determine the significance of the dummy variable to the model.

House
Assessed Value ($000)
Size of House (Thousands of Square Feet)
Age (Years)
1 184.4 2.00 3.42
2 177.4 1.71 11.50
3 175.7 1.45 8.33
4 185.9 1.76 0.00
5 179.1 1.93 7.42
6 170.4 1.20 32.00
7 175.8 1.55 16.00
8 185.9 1.93 2.00
9 178.5 1.59 1.75
10 179.2 1.50 2.75
11 186.7 1.90 0.00
12 179.3 1.39 0.00
13 174.5 1.54 12.58
14 183.8 1.89 2.75
15 176.8 1.59 7.17

Suppose that the service time at a store with only, one check-out counter is Exponentially distributed, with a mean time of 10 minutes.

a) What is the probability that a customer who is first in line now will spend more than 15 minutes waiting in the check-out line? (Solve using Exponential distribution and then using Poisson.)

b) A customer has already been waiting in the line for more than 10 minutes. What is the probability that this customer will still be at the store in more than 15 minutes from now?

c) What is the probability of spending less than a half an hour at the check-out? (Solve using two different time units.)

Suppose you want to know if different dosages of caffeine affect students’ performance on a test. We randomly sampled 15 college students and randomly assigned them to three conditions.

• Group 1: Very large dose of caffeine
• Group 2: Moderate dose of caffeine
• Group 3: Placebo (no caffeine)

The table below displays these 15 students’ scores.

1. Calculate SSB, SSW, SST, MSB, MSW, and F observed value. Fill out the blanks of this table.

Roberta wants to compare productivity, as measured by the number of customers served, among three workers. The number of customers served by each worker is shown below.

1. Is there a difference in the number of customers served? The level of significance is 0.01. Show all the five steps of the hypothesis testing.

1. You ask her what was the experimental unit and were the experimental units randomized. She is unfamiliar with these concepts. Please explain experimental unit and the need for randomization of the experimental units to the treatment combinations to her.

2. You decide to analyze the experiment as a 3 X 3 factorial arrangement using a completely randomized design and obtain the following ANOVA tables.

Analysis of Variance Table

Response: diastolic

          Df Sum Sq Mean Sq F value   Pr(>F)  

diet       2 322.83 161.42 4.2055 0.032819 *

drug       2 811.06 405.53 10.5655 0.001042 **

diet:drug 4 155.76   38.94 1.0145 0.427585  

Residuals 17 652.50   38.38                   

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Anova Table (Type II tests)

Response: diastolic

          Sum Sq Df F value   Pr(>F)  

diet      379.50 2 4.9437 0.020307 *

drug      811.06 2 10.5655 0.001042 **

diet:drug 155.76 4 1.0145 0.427585  

Residuals 652.50 17                   

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Anova Table (Type III tests)

Response: diastolic

            Sum Sq Df   F value    Pr(>F)   

(Intercept) 185050 1 4821.2144 < 2.2e-16 ***

diet           375 2    4.8838 0.021093 *

drug           796 2   10.3735 0.001136 **

diet:drug      156 4    1.0145 0.427585   

Residuals      652 17                       

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

a. For this analysis, which of the SS methods would you choose? Explain why?

b. The lack of a sign diet X drug interaction indicates __________________?

1

Start Excel. Download and open the file named exploring_ecap_grader_a1.xlsx.

2

On the DC worksheet, select the range A4:G4, wrap the text, apply Center alignment, and apply Blue, Accent 5, Lighter 60% fill color.

3

On the DC worksheet, merge and center the title in the range A1:G1. Apply Accent5 cell style and bold to the title.

4

On the DC worksheet, change the width of column A to 34.

5

On the DC worksheet, select the range C5:F10 and insert Line Sparklines in the range G5:G10.

6

On the DC worksheet, select the range G5:G10, display the high point sparkline marker, and change the color of the high point markers to Dark Blue.

7

On the DC worksheet, select the range G5:G10, apply Same for All Sparklines for both the vertical axis minimum and maximum values.

8

On the DC worksheet, select the ranges A4:A10 and C4:F10 and create a clustered bar chart. Apply the Color 16 chart color. Apply the gradient fill to the plot area. Do not change the default gradient options.

Note, depending on the version of Office used, the chart color may be named Monochromatic Palette 12.

9

Position the top-left corner of the chart in cell A13. Change the chart height to 6 inches and the chart width to 7 inches.

10

Change the chart title to Annual Visitors. Apply Blue, Accent 5, Darker 25% font color to the chart title and category axis labels. Change the value axis display units to Millions.

11

Apply data labels to the outside end of the 2015 data series. Apply Number format with 1 decimal place to the data labels.

12

Click the Places sheet tab, convert the data to a table, and apply Table Style Medium 6.

13

On the Places worksheet, sort the data by City in alphabetical order and then within City, sort by Sightseeing Locations in alphabetical order.

14

On the Places worksheet, add a total row to display the average of the Time Needed column. Apply Number format with zero decimal places to the total.

15

On the Places worksheet, select the values in the Time Needed column and apply conditional formatting to highlight cells containing values greater than 60 with Green Fill with Dark Green Text.

16

On the Places worksheet, apply a filter to display only fees that are less than or equal to $10.

17

On the Cities worksheet, click cell F4 and enter a formula that will subtract the Departure Date (B1) from the Return Date (B2) and then multiply the result by the Rental Car per Day value (F3).

18

On the Cities worksheet, click cell E13. Depending on the city, you will either take a shuttle to/from the airport or rent a car. Insert an IF function that compares to see if Yes or No is located in the Rental Car? Column for a city. If the city contains No, display the value in cell F2. If the city contains Yes, display the value in the Rental Car Total (F4). Copy the function from cell E13 and use the Paste Formulas option to copy the function to the range E14:E18 without removing the border in cell E18.

19

On the Cities worksheet, click cell F13. The lodging is based on a multiplier by City Type. Some cities are more expensive than others. Insert a VLOOKUP function that looks up the City Type (B13), compares it to the City/COL range (A7:B10), and returns the COL percentage. Then multiply the result of the lookup function by the Total Base Lodging (B5) to get the estimated lodging for the first city. Copy the function from cell F13 and use the Paste Formulas option to copy the function to the range F14:F18 without removing the border in cell F18.

20

On the Cities worksheet, click cell H13 and enter the function that calculates the total costs for the first city. Copy the function in cell H13 and use the Paste Formulas option to copy the function to the range H14:H18 without removing the border in cell H18.

21

On the Cities worksheet, select the range E14:H18 and apply Comma Style with zero decimal places. Select the range E13:H13 and apply Accounting Number format with zero decimal places.

22

On the Cities worksheet, in cell I2, enter a function that will calculate the average total cost per city. In cell I3, enter a function that will identify the lowest total cost. In cell I4 enter a function that will return the highest total cost.

23

On the Cities worksheet, select Landscape orientation, set a 1-inch top margin, and center the worksheet data horizontally on the page.

24

Ensure that the worksheets are correctly named and placed in the following order in the workbook: DC, Places, Cities. Save the workbook. Close the workbook and then exit Excel. Submit the workbook as directed.