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2. BRIEF SOLUTIONS (2 MARKS EACH Give the numeric value of each of the following limits if it exists; if the limit is too or -o, write too or-o respectively. In all other cases write "NO FINITE OR INFINITE LIMIT”. 1 1 (a) lim arctan (1- x 21+ ANSWER ONLY

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9 Nov 2018
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

QUESTION 1What is the purpose of post hoc tests? Under what circumstances are post hoc tests not needed or appropriate?

a. Under what circumstances is ANOVA a more appropriate statistical technique to use than a t test for independent samples? Please provide an example(s) to support your answer. (2 marks)

b.  (2 marks)

c. In testing the difference between group means, how are between group and within group variability related to each other? Provide an example to support your answer. (2 marks)

QUESTION 2

a. If a two-factor ANOVA results in a significant main effect for factor A and a significant AxB interaction, explain why you should be cautious in interpreting the effect of factor A. (1 mark)

b. For the following research situations what would be your main effects and interaction effect. If there was a significant interaction effect what would that mean? (please be as clear as possible in your explanation):

  1. A researcher hypothesizes that the effect of alcohol consumption on one’s motor skills depends on the person’s weight (underweight, normal, overweight), but that this may differ for men versus women. (2 marks)

  2. A teacher is interested in seeing how attending class and reading the assigned chapters is related to her students’ performance on tests. She assesses each student in terms of how often they attend class (rarely, sometimes, regularly) and how often they read the assigned chapters (rarely, sometimes, regularly). (2 marks)

1

QUESTION 3

Ethel is interested in two methods of note-taking strategies and the effect of these strategies on the overall GPAs of college freshmen. She believes that men would benefit most from Method 1, while women would benefit most from Method 2. After obtaining 30 men and 30 women volunteers in freshmen orientation, she randomly assigns 10 men and 10 women to Method 1, 10 men and 10 women to Method 2, and 10 men and 10 women to a control condition. During the first month of the spring semester individuals in the two note-taking method groups receive daily instruction on the particular note-taking method to which they were assigned. The control group receives no note-taking instruction. Fall and spring GPAs for all participants are recorded and a score that is the difference between the spring and fall semester GPAs is calculated.

Below are the results from running a two-way ANOVA. Please answer the following:

  1. What is the dependent variable? (0.5 marks)

  2. What are the independent variables (factors)? (0.5 marks)

  3. What is the research question(s) being addressed? (1 mark)

  4. What does the descriptive statistics (graphical) tell us about the effects under study?

    (1 mark)

  5. What assumptions are being tested in the R output? Are these assumptions met? Please

    provide statistical evidence. (2 marks)

  6. What effects are being tested in the R output? (1 mark)

  7. What does output from the ANOVA table tell us? (1 mark)

  8. What type of follow-up analyses was conducted and why? Please interpret. (2 marks)

2

: Men
: Method1

      median
coef.var

0.300

0.469

: Women
: Method1

      median
coef.var

0.150

0.496

: Men
: Method2

      median
coef.var

0.275

0.027

: Women
: Method2

      median
coef.var

0.600

0.629

: Men
: Control

      median
coef.var

0.175

mean 0.335

mean 0.170

mean 0.305

mean 0.640

mean 0.165

mean 0.105

skew.2SE
   0.408

SE.mean CI.mean.0.95

var 0.052

var 0.033

var 0.037

var 0.032

var 0.022

var 0.021

normtest.W
     0.936

std.dev
  0.229

0.682
    skewness

1.076
    skewness

0.630
    skewness

0.072

SE.mean CI.mean.0.95

normtest.p 0.830 -----------------------------------------------------------------------------

skew.2SE
   0.342

kurtosis
  -0.645

kurt.2SE
  -0.242

normtest.W
     0.964

0.058

SE.mean CI.mean.0.95

std.dev
  0.183

normtest.p 0.096 -----------------------------------------------------------------------------

skew.2SE
   0.361

kurtosis
  -1.363

kurt.2SE
  -0.511

normtest.W
     0.869

0.061

SE.mean CI.mean.0.95

std.dev
  0.192

normtest.p 0.857 -----------------------------------------------------------------------------

0.278
    skewness

0.904
    skewness

skew.2SE
  -0.124

kurtosis
  -1.096

kurt.2SE
  -0.411

normtest.W
     0.979

-0.171

: Women
: Control

      median
coef.var

0.100

1.392
    skewness

0.560

0.046

kurtosis
  -0.759

0.105

kurt.2SE
  -0.284

   std.dev
     0.146

normtest.p
     0.512

skew.2SE
   0.019

kurtosis
  -1.443

kurt.2SE
  -0.541

normtest.W
     0.967

skew.2SE
   0.458

kurtosis
  -0.770

kurt.2SE
  -0.289

normtest.W
     0.906

0.056

SE.mean CI.mean.0.95

std.dev
  0.178

normtest.p 0.254 -----------------------------------------------------------------------------

                                                                      std.dev
                                                                        0.149

normtest.p 0.958 -----------------------------------------------------------------------------

0.047

SE.mean CI.mean.0.95

0.164

0.131

0.137

0.127

0.107

3

> leveneTest(gpa$gpaimpr~gpa$gender, data=gpa,center=mean)

Levene's Test for Homogeneity of Variance (center = mean) Df F value Pr(>F)

group 1 7.09 0.01* 58

---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > leveneTest(gpa$gpaimpr~method, data=gpa,center=mean) Levene's Test for Homogeneity of Variance (center = mean)

      Df F value Pr(>F)
group  2    1.94   0.15

57

> #running Levene's test for assumption of HOV (INTERACTION EFFECT)
> leveneTest(gpa$gpaimpr, interaction(gpa$gender,gpa$method),center=mean) Levene's Test for Homogeneity of Variance (center = mean)

      Df F value Pr(>F)
group  5    0.57   0.72

54

Df Sum Sq Mean Sq F value Pr(>F) gender 1 0.020 0.020 0.61 0.43753

method 2 1.174 0.587 17.81 1.1e-06 *** gender:method 2 0.695 0.348 10.54 0.00014 *** Residuals 54 1.780 0.033
---

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

4

gender        0.0055
method        0.3200
gender:method 0.1894

0.011
0.397
0.281

eta.sq eta.sq.part

#selecting only Method1, run ANOVA, then follow-up tests

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = gpaimpr ~ gender, data = gpaMethod1)
$`gender`
Women-Men -0.165 -0.3594851  0.02948506    0.0915581

diff        lwr        upr     p adj

#selecting only Method2, run ANOVA, then follow-up tests

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = gpaimpr ~ gender, data = gpaMethod2)
$`gender`
Women-Men 0.335 0.161153 0.508847   0.000754

diff      lwr      upr    p adj

5

Opeele Kyinkafa sells different used 2005 GM cars in excellent condition. The value or the retail price (Price) of a car is dependent on a variety of characteristics such as number of miles the car has been driven (Mileage), manufacturer of the car (Make) such as Buick, Cadillac, Chevrolet, Pontiac, SAAB, and Saturn. The car price is also influenced by the body type (Type) such as sedan, convertible, coupe, hatchback and wagon. It is also affected by number of cylinders (Cylinders) in the engine, the engine size (Liter), cruise control which is an indicator variable representing whether the car has cruise control (yes) or no otherwise and Sound indicator representing whether the car has upgraded speakers (yes) or no otherwise. All cars in this data set were less than one year old when priced and considered to be in excellent condition. Determine which major variables are dummies and are dynamic? Identify 3 potential unobserved heterogenous factors in this dataset. Display the full descriptive statistics of the data in R. Why do you think some variables are starred (*)? What is the median for “price”, standard deviation for “mileage”, skewness for “cylinder” and mean for “sound”? Test if “price” is normally distributed using histogram, kernel density plot and the shapiro wilk test. Create a red scatterplot matrix of price, mileage, cylinder, liter, make. From your graph, is the correlation between price & mileage positive or negative? What’s the pearson correlation coefficient between price & mileage and between “cylinder” & “liter” correct to 2 d.p Create a correlation matrix of the dataset by finding the apt R command for converting all string/dummy variables From the matrix, identify 2 potentially good predictors? Identify 3 pairs of variables that are mostly multicollinear. Which 2 pairs of variables are least correlated? Identify 3 pairs of variables most highly correlated with Cylinder Generate a simple regression plot of price on mileage with a re fitted line. Run the whole multiple regression model (label the equation as "regprice") & use it to answer the other questions. Specify the regression model for the whole data keeping the exact names of the variables. Write the estimated regression equation. In one sentence, which variables are significant and which are not? Justify Is the regression model justifiable? Explain Interpret the coefficient of Mileage, MakeCadillac, TypeSedan, Cylinder, & Cruiseyes. Compare the price of a car with 130,000 mileage, 6 cylinders, 3.8 liters, with cruise and sound, was manufactured by Pontiac with a convertible body type with that of the price of a car with four cylinders, 120,000 mileage, 3.8 liters, without cruise nor sound, was manufactured by Cadillac with a hatchback body type. Which factor(s) appears to be causing a comparative difference (if any)? Using only the VIF, which one of the pairs of variables selected to be multicollinear may be deleted? Justify?

EX16_XL_CH05_GRADER_CAP_AS - Travel Expenses 1.3

Project Description:

You are the manager of an information technology (IT) team. Your employees go to training workshops and national conferences to keep up-to-date in the field. You created a list of expenses by category for each employee for the last six months. Now you want to subtotal the data to review total costs by employee and then create a PivotTable to look at the data from different perspectives.

Instructions:

For the purpose of grading the project you are required to perform the following tasks:

Step

Instructions

Points Possible

1

Start Excel. Open the downloaded Excel file named exploring_e05_grader_a1_Expenses.xlsx. Save the workbook as exploring_e05_grader_a1_Expenses_LastFirst, replacing LastFirst with your own name.

0.000

2

On the Subtotals worksheet, sort the data by Employee and further sort by Category, both in alphabetical order.

4.000

3

Use the Subtotals feature to insert subtotal rows by Employee to calculate the total expense by employee.

5.000

4

Collapse the Donaldson and Hart sections to show only their totals. Leave the other employees’ individual rows displayed.

5.000

5

Use the Expenses worksheet to create a blank PivotTable on a new worksheet named Summary. Name the PivotTable Categories.

8.000

6

Use the Category and Expense fields, enabling Excel to determine where the fields go in the PivotTable.

5.000

7

Modify the Values field to determine the average expense by category. Change the custom name to Average Expense.

4.000

8

Format the Values field with Accounting number type.

3.000

9

Type Category in cell A3 and change the Grand Totals layout option to On for Rows Only.

5.000

10

Apply Pivot Style Dark 2 and display banded rows.

Note, depending upon the version of Office being used, the style name may be Light Blue, Pivot Style Dark 2.

5.000

11

Insert a slicer for the Employee field, change the slicer height to 2 inches and apply the Slicer Style Dark 5. Move the slicer below the PivotTable.

Note, depending upon the version of Office being used, the style name may be Light Blue, Slicer Style Dark 5.

5.000

12

Use the Expenses worksheet to create another blank PivotTable on a sheet named Totals. Add the Employee to the Rows and add the Expense field to the Values area. Sort the PivotTable from largest to smallest expense.

10.000

13

Change the name for the Expenses column to Totals and format the field with Accounting number format.

4.000

14

Insert a calculated field to subtract 2659.72 from the Expense field. Format the field with the custom name Above or Below Average and apply Accounting number format to the field.

10.000

15

Set 12.25 width for column B and column C, change the row height of row 3 to 30, and apply word wrap to cell C3.

4.000

16

Create a clustered column PivotChart from the PivotTable. Move the PivotChart to a new sheet named Chart. Hide all field buttons in the PivotChart, if necessary.

Note, Mac users, select the range A3:C8 in the PivotTable. On the Insert tab, click Recommended Charts, and then click Clustered Column to make the chart.

10.000

17

Add a chart title above the chart and type Expenses by Employee. Change the chart style to Style 14.

6.000

18

Apply 11 pt font size to the value axis and display vertical axis as Accounting with zero decimal places.

4.000

19

Create a footer on all worksheets with your name in the left section, the sheet name code in the center section, and the file name code in the right section.

3.000

20

Ensure that the worksheets are correctly named and placed in the following order in the workbook: Subtotals, Summary, Chart, Totals, Expenses. Save the workbook. Close the workbook and then exit Excel. Submit the workbook as directed.

0.000
 

Total Points

100.000

https://www.dropbox.com/s/m7falnl85tfazl9/Torres%20DaSilva_exploring_e05_grader_a1_Expenses.xlsx?dl=0

 
 

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