MGMT 650 Fall 2016 Problem Set 5
1. UMUC wants to use a new tutorial to teach the students about business ethics. As an experiment the administrator randomly selected 15 students and randomly assigned them to one of three groups which include either a PowerPoint presentation created by the faculty, AuthorGen Presentation created by the faculty, or a well known tutorial by the ABC company. After completing their assigned tutorial, the students are given a Business Ethics test. At the .01 significance level, can UMUC conclude that there is a difference between how well the different tutorials work for the students?
Note: (Here is a good website where you can find the f table for significance level .01 http://www.socr.ucla.edu/Applets.dir/F_Table.html#FTable0.01)
PowerPoint Tutorial (X1) |
AuthorGen Tutorial (X2) |
ABC Tutorial (X3) |
68 |
79 |
75 |
85 |
86 |
83 |
91 |
82 |
78 |
87 |
92 |
86 |
88 |
91 |
81 |
2. Graph each set of data and determine if there is a correlation and how strong it is. State if that relationship is negative or positive.
- Highest Grossing movies and the year they were released.
$2,186.80 |
1997 |
$2,068.20 |
2015 |
$1,670.40 |
2015 |
$1,519.60 |
2012 |
$1,516.00 |
2015 |
$1,405.40 |
2015 |
$1,341.50 |
2011 |
$1,276.50 |
2013 |
$1,215.40 |
2013 |
$1,159.40 |
2015 |
$1,151.10 |
2016 |
$1,123.80 |
2011 |
$1,119.90 |
2003 |
$1,108.60 |
2012 |
$1,104.10 |
2014 |
$1,084.90 |
2012 |
$1,066.20 |
2006 |
$1,063.20 |
2010 |
$1,045.70 |
2011 |
$1,029.20 |
1993 |
$1,027.00 |
1999 |
$1,025.50 |
2010 |
$1,022.60 |
2016 |
$1,021.10 |
2012 |
$1,004.60 |
2008 |
$974.80 |
2001 |
$970.80 |
2013 |
$968.50 |
1994 |
$963.40 |
2007 |
$960.30 |
2010 |
$958.40 |
2013 |
$956.00 |
2014 |
$939.90 |
2007 |
$937.90 |
2016 |
$936.70 |
2003 |
$934.40 |
2009 |
$926.00 |
2002 |
$919.80 |
2004 |
$896.90 |
2005 |
$890.90 |
2007 |
$886.70 |
2009 |
$880.70 |
2015 |
$879.00 |
2002 |
$877.20 |
2012 |
$872.70 |
2016 |
$871.50 |
2001 |
$865.00 |
2013 |
$857.40 |
2015 |
$848.80 |
2005 |
$836.30 |
2009 |
$829.70 |
2012 |
$825.50 |
2010 |
$821.70 |
2002 |
$817.40 |
1996 |
$799.00 |
2007 |
$796.70 |
2004 |
$792.90 |
1982 |
$788.70 |
2013 |
$786.60 |
2008 |
$783.80 |
2004 |
$782.40 |
2016 |
$775.40 |
1977 |
$773.30 |
2014 |
$769.70 |
2009 |
$758.50 |
2014 |
$758.20 |
2006 |
$757.90 |
2012 |
$755.40 |
2014 |
$752.60 |
2010 |
$747.90 |
2014 |
$746.90 |
2012 |
$745.00 |
2005 |
$743.60 |
2013 |
$742.10 |
2003 |
$731.30 |
2009 |
$727.60 |
2016 |
$723.20 |
2013 |
$714.40 |
2014 |
$712.20 |
2011 |
$710.60 |
2014 |
$709.70 |
2009 |
$709.70 |
2007 |
$709.00 |
2014 |
$698.50 |
2010 |
$694.70 |
2011 |
$694.40 |
2012 |
$682.30 |
2015 |
$677.90 |
1994 |
$675.10 |
2014 |
$672.80 |
1999 |
$668.00 |
2013 |
$665.70 |
2011 |
$660.90 |
2006 |
$657.80 |
2014 |
$654.30 |
2003 |
$653.40 |
2015 |
$649.40 |
2002 |
$644.60 |
2013 |
$631.70 |
2008 |
- Hours studied and test grade
3 |
75 |
5 |
90 |
2 |
75 |
6 |
80 |
7 |
90 |
1 |
50 |
2 |
65 |
7 |
85 |
1 |
40 |
7 |
100 |
2 |
70 |
6 |
85 |
7 |
85 |
1 |
70 |
5 |
80 |
5 |
85 |
5 |
80 |
3 |
50 |
3 |
60 |
9 |
95 |
5 |
75 |
6 |
80 |
2 |
50 |
5 |
65 |
2 |
40 |
3 |
70 |
8 |
80 |
4 |
75 |
5 |
60 |
6 |
95 |
- Humidity level and time spent outside
50% |
6 |
40% |
7 |
70% |
0.5 |
20% |
4.5 |
90% |
0.25 |
30% |
4 |
70% |
5.5 |
30% |
2 |
20% |
2 |
30% |
2.75 |
40% |
2.75 |
10% |
8.5 |
90% |
1 |
70% |
2.2 |
80% |
1.5 |
50% |
3 |
70% |
1.25 |
40% |
4 |
30% |
3.75 |
20% |
6 |
20% |
5 |
70% |
2.5 |
70% |
2 |
80% |
1 |
50% |
4 |
3. ASPCA wanted to find out if there was a relationship between the type of animals preferred and the gender of the owner. They gathered data from 50 randomly chosen pet owners who owned either one cat or one dog:
gender |
type |
gender |
type |
female |
cat |
male |
cat |
male |
dog |
female |
cat |
male |
dog |
male |
cat |
male |
dog |
female |
dog |
female |
cat |
female |
cat |
female |
cat |
female |
dog |
female |
dog |
male |
cat |
female |
cat |
male |
dog |
male |
dog |
male |
dog |
female |
dog |
male |
dog |
female |
dog |
male |
cat |
male |
dog |
female |
dog |
male |
cat |
female |
cat |
male |
cat |
male |
dog |
female |
dog |
female |
cat |
female |
cat |
female |
cat |
female |
cat |
male |
cat |
female |
cat |
female |
cat |
female |
dog |
male |
dog |
male |
cat |
female |
dog |
male |
dog |
male |
cat |
male |
cat |
female |
dog |
male |
dog |
male |
cat |
male |
dog |
male |
cat |
female |
dog |
male |
dog |
Use Excel’s capabilities to create a pivot table that shows the number of pets owned by each gender.
4. Use the pivot table from problem 1 to find the Chi Square value and give the interpretation based on a .01 significance level. Is there are relationship between the sex of the owner and the type of pet they prefer?
Here is a website with a chi square table:
http://sites.stat.psu.edu/~mga/401/tables/Chi-square-table.pdf
5. A human resources director wants to find out if there is a pattern with the day of the week and the number of times employees were sick on that day. She tallied the number of times 60 employees were absent on these days:
Monday: 12
Tuesday: 9
Wednesday: 11
Thursday: 10
Friday: 9
Saturday: 9
Using a significance level of .05:
- What is the null and alternative hypotheses?
- What is the chi square value for this scenario?
- What is the critical value of chi square ?
- Find the p value.
- Is there evidence to suggest that some employees are more likely to be sick on certain days of the week?
6. A CEO of a large pharmaceutical company would like to determine if he should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling asthma. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called XBC and the number of orders received. The manufacturing process of this drug is very difficult and requires stability so the CEO would prefer to generate a stable number of orders. The cost of advertising is always an important consideration in the phase I roll-out of a new drug. Data that have been collected over the past 20 months indicate the amount of money spent of television advertising and the number of orders received.
The use of linear regression is a critical tool for a manager’s decision-making ability. Please carefully read the example below and try to answer the questions in terms of the problem context. Here are the results of the data collection.
Month |
Advertising cost (in thousands) |
# of orders |
1 |
$68.93 |
4,902,000 |
2 |
72.62 |
3,893,000 |
3 |
79.58 |
5,299,000 |
4 |
58.67 |
4,130,000 |
5 |
69.18 |
4,367,000 |
6 |
70.14 |
5,111,000 |
7 |
83.37 |
3,923,000 |
8 |
68.88 |
4,935,000 |
9 |
82.99 |
5,276,000 |
10 |
75.23 |
4,654,000 |
11 |
81.38 |
4,598,000 |
12 |
52.9 |
2,967,000 |
13 |
61.27 |
3,999,000 |
14 |
79.19 |
4,345,000 |
15 |
80.03 |
4,934,000 |
16 |
78.21 |
4,653,000 |
17 |
83.77 |
5,625,000 |
18 |
62.53 |
3,978,000 |
19 |
88.76 |
4,999,000 |
20 |
72.64 |
5,834,000 |
- Set up a scatter diagram and calculate the associated correlation coefficient. Discuss how strong you think the relationship is between the amount of money spent on television advertising and the number of orders received. Please use the Scatterplot and Correlation procedures within Excel under Tools > Data Analysis
- Is there a statistically significant relationship between the two variables at alpha = .05? How do you know?
- What is the regression equation?
- Interpret the meaning of the slope, b1, in the regression.
- Predict the monthly advertising cost when the # of orders is 5,100,000.
- Compute the coefficient of determination, Rsquare, and interpret its meaning.
- Compute the standard error of estimate, and interpret its meaning.
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