Problem Set: Week Two Complete the problems below and submit your work in one Word document. Be sure to show all of your work and clearly label all calculations. Calculations completed in Excel must...

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Problem Set: Week Two
Complete the problems below and submit your work in one Word document. Be sure to show all of your work and clearly label all calculations. Calculations completed in Excel must be copied and pasted into a single Word document. No Excel documents will be graded.


  1. Problem One

    Suppose that an automotive parts and accessories chain is experimenting with a new sales promotion. Two similar stores are selected for the experiment. For Store 1, nothing changes. This store constitutes the control group. For Store 2, the treatment group, the promotion is implemented.
    Sales in hundreds of dollars over a five-day period are as follows:



  1. Control: 6, 6, 7, 10, 12, 9, 6, 5, 5, 7

  2. Treatment: 2, 5, 2, 4, 7, 1, 2, 3, 4, 5



The expectation that sales will be higher in the treatment group makes this a one-tailed test; the alternate hypothesis is m1

Show all of your work and clearly label each of your calculations. Share your calculations and your interpretations of your findings in your Word document.



  1. Problem Two.


    Suppose that a home builder is approached by a customer who wants to move in as soon as possible. The customer chooses three home designs that she likes and asks the home builder which one could be completed the fastest. To compare the three designs on speed of completion, the builder randomly selects 10 homes that he built in the past based on each of the three designs.
    Use the Excel Analysis ToolPak to run an ANOVA test in order to determine which design would be best for the customer. Show all of your work and clearly label each of your calculations. Make sure to also clearly describe the respective data and your conclusions.
    The data for the number of days to build each home are as follows:



  1. Design A: 15, 17, 19, 21, 23, 25, 27, 29, 31, 33

  2. Design B: 29, 34, 39, 44, 49, 54, 59, 64, 69, 74

  3. Design C: 22, 24, 25, 27, 28, 28, 29, 31, 33, 34



For more information on conducting an ANOVA test in Excel reference the Week Two Recommended Resources.



  1. Problem Three

    An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. Now there are concerns that if the true mean is actually higher than this they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set significance level = :05, test to see if the insurance company should be concerned.
    Show all of your work and clearly label each of your calculations. Share your calculations from Excel and your interpretations of your findings in your Word document.

    Copy and paste your calculations for the three problems from Excel to Word and submit one Word document with your clearly labeled calculations and interpretations.











Interval Data



4.
Problem 4

A courier service in a large city tracks the number of deliveries they are asked to make by 10 clients both before and after offering a progressive discount for repeat business. Their goal is to assess the effects of the discount.


  1. What is the most appropriate statistical test in this situation? Why?

  2. Are there significant differences in the number of deliveries?

  3. If the goal is to promote repeat business, should the discount be continued?









Correlation



5.
Problem 5

An employment agency gathers the following data on its clients:

  1. Age

  2. Gender

  3. Educational level (no high school, high school, associate’s, bachelor’s, master’s)

  4. Years of past experience

  5. Whether or not they have been successfully placed in employment by the agency



Additionally, the following data is gathered for those who have been successfully placed:

  1. Starting salary

  2. Current salary

  3. Tenure in months



Based on the information above answer the following questions:

  1. Which type of correlation procedure would be most appropriate to gauge the relationship between each pair of variables?

  2. Do you expect each pair of variables to be significantly correlated or not? Why?

  3. For the variables you expect to be significantly correlated, what do you expect the direction of the relationship to be? Why?

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Answered Same DayDec 23, 2021

Answer To: Problem Set: Week Two Complete the problems below and submit your work in one Word document. Be sure...

David answered on Dec 23 2021
121 Votes
Problem Set: Week Two
Complete the problems below and submit your work in one Word document. Be sure to show all of your work and clearly label all calculations. Calculations completed in Excel must be copied and pasted into a single Word document. No Excel documents will be graded.
1. Problem One
Suppose that an automotive parts and accessories chain is experimenting with a new sales promotion. Two similar stores are selected for the experiment. For Store 1, nothing changes. This store constitutes the control group. For Store 2, the treatment group, the promotion is implemented.
Sales in hundreds of dollars over a five-day period are as follows:
a. Control: 6, 6, 7, 10, 12, 9, 6, 5, 5, 7
b. Treatment: 2, 5, 2, 4, 7, 1, 2, 3, 4, 5
The expectation that sales will be higher in the treatment group makes this a one-tailed test; the alternate hypothesis is m1 < m2. Use Excel to determine whether differences between the two groups are statistically significant.
Show all of your work and clearly label each of your calculations. Share your calculations and your interpretations of your findings in your Word document.
Solution:
    t-Test: Two-Sample Assuming Equal Variances
    
    
    
     
    Control
    Treatment
    Mean
    7.3
    3.5
    Variance
    5.344444
    3.388889
    Observations
    10
    10
    Pooled Variance
    4.366667
    
    Hypothesized Mean Difference
    0
    
    df
    18
    
    t Stat
    4.066245
    
    P(T<=t) one-tail
    0.000362
    
    t Critical one-tail
    1.734064
    
    P(T<=t) two-tail
    0.000725
    
    t Critical two-tail
    2.100922
     
Null Hypothesis (Ho): m1 ≥ m2
Alternative Hypothesis (Ha): m1 < m2
Test Statistics
t = 4.066
P-value = 0.00036
Since p-value is less than 0.05, we reject the null hypothesis.
There is sufficient evidence to conclude that the expectation that sales will be higher in the treatment group.
2. Problem Two.
Suppose that a home builder is approached by a customer who wants to move in as soon as possible. The customer chooses three home designs that she likes and asks the home builder which one could be completed the fastest. To compare the three designs on speed of completion, the builder randomly selects 10 homes that he built in the past based on each of the three designs.
Use the...
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