Assignments 2 | Complete Solution

Assignment 2

Your assignment should be submitted electronically. If you have problems writing formulas with your word processor, cite the formula number as it appears in textbook. Show your work! Part marks are awarded only when detailed solutions are presented. If only the answers are given, you will not receive any marks for incorrect answers. You should submit solutions showing main calculations (i.e., procedures, formulas, and conclusions) for each and every problem. Occasionally, an answer is wrong due to an arithmetic and/or computation error, yet you could still get part marks if the formulas and procedures are correct.

Note:  You can use the Insert/Equation function to add complex math to a Microsoft Word document. Be aware, though, that adding equations increases the size of your files.

Question 1                                         [4 marks]
Consider the following information.
    2000    2003
Item    Price    Quantity    Price    Quantity
A    $  .25    210    $  .37    210
B       .87       2      1.15       2
C     10.00       4     15.00       4
D       .35     35       .60     35
    
    a.    Compute the Laspeyres index.
    b.    Compute the Paasche index.
    c.    Comment on your answers for Parts c and d.

Question 2                                     [6 marks]
The following time series shows the sales of a clothing store over a 10-week period.
    Sales
    Week    ($1,000s)

    1    15
    2    16
    3    19
    4    18
    5    19
    6    20
    7    19
    8    22
    9    15
    10    21

    a.    Compute a 4-week moving average for the above time series.
    b.    Compute the mean square error (MSE) for the 4-week moving average forecast.
    c.    Use  = 0.3 to compute the exponential smoothing values for the time series.
    d.    Forecast sales for week 11.
 

Question 3                                         [5 marks]
Fifteen people were asked to indicate their preference for domestic versus imported cars.  The following data showed their preferences.
    Individual    Domestic vs. Imported
    1    +
    2    +
    3    -
    4    +
    5    +
    6    +
    7    -
    8    +
    9    +
    10    +
    11    +
    12    +
    13    +
    14    +
    15    -

With  = 0.05, test for a significant difference in the preferences for cars.  A "+" indicates a preference for imported cars.

Question 4                                         [5 marks]
Two faculty members ranked 12 candidates for scholarships. Calculate the Spearman rank-correlation coefficient and test it for significance.  Use a .02 level of significance.
    Rank by    Rank by
    Candidate    Professor A    Professor B

    1    6    5

    2    10    11

    3    2    6

    4    1    3

    5    5    4

    6    11    12
    7    4    2
    8    3    1
    9    7    7
    10    12    10
    11    9    8
    12    8    9

Question 5                                         [5 marks]
Independent random samples of ten day students and ten evening students at a university showed the following age distributions.
    Day    Evening
    26    32
    18    24
    25    23
    27    30
    19    40
    30    41
    34    42
    21    39
    33    45
    31    35

Use  = 0.05 and test for any significant differences in the age distribution of the two populations. Use Wilcoxon Signed-Rank Test.

Question 6                                         [5 marks]
A production process that is in control has a mean () of 80 and a standard deviation () of 10.
    a.    Determine the upper and the lower control limits for sample sizes of 25.
    b.    Five samples had means of 81, 84, 75, 83, and 79.  Construct an X bar chart and explain whether or not the process is in control.