Refer to the following table which contains the sales

The following information refers to the next two questions:
Refer to the following table which contains the sales (in $,000) for a department store for the first ten months of the year.
Month Sales
January 440
February 480
March 590
April 400
May 500
June 550
July 470
August 500
September 600
October 520

QUESTION 16
Using a three period moving average (i.e. MA(3)) as a forecasting method, what is the MSE for this forecasting model?
Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.
Please do NOT include any units in your answer.

QUESTION 17
Using simple exponential smoothing (with a smoothing constant of 0.2) as a forecasting method, what is the MSE for this forecast model?
Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.

The following information refers to the next question:
A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is fifty (50) minutes with a standard deviation of forty (40) minutes (the very large standard deviation is due to a variety of factors including a large variation in skills amongst the ‘Do it yourself’ home handyman which is traditionally one of the companies customer base). Suppose a random sample of 64 purchasers of this table saw is taken.

QUESTION 19
What is the probability that the sample mean will be less than 44 minutes __________?
Answer should be to four decimal places which is consistent with the number of decimal places listed in your appendix tables e.g. 0.1234 etc.

The next six questions refer to the following information:
(All calculations should be to at least three decimal places)
The tourist industry is subject to enormous seasonal variation. A hotel in North Queensland has recorded its occupancy rate for each quarter during the past 5 years. These data are shown in the accompanying table.
Table 1: Occupancy rate
Year
2004 2005 2006 2007 2008
Quarter 1 0.261 0.295 0.312 0.362 0.396
Quarter 2 0.302 0.324 0.345 0.388 0.418
Quarter 3 0.502 0.568 0.598 0.696 0.782
Quarter 4 0.568 0.615 0.698 0.738 0.802

QUESTION 30
What is the centred moving average that would correspond to Quarter 4 in 2006?
Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.
Please do NOT include any units in your answer.

QUESTION 31
What is the adjusted seasonal index for Quarter 4 __________%?
Answer should be listed to three decimal places in the form 0.123 i.e. 0.123 represents 12.3%, 1.234 represents 123.4% etc.
Please do NOT include the units (%) in your answer.

QUESTION 32
The trend line for this decomposition model can be read off the partial regression printout (at 5 decimal places) to be Y = 0.36806 + 0.01195 T where T represents time.

Analysing the partial regression printout, what is the coefficient of determination (R2) for this trend line? (Select the closest correct answer).

0.2973 (i.e. 29.73%)

0.5452 (i.e. 54.52%)

0.7165 (i.e. 71.65%)

0.9886 (i.e. 98.86%)
QUESTION 33
What would be the forecast in Quarter 4, 2009 using the trend line given previously (recall that to three decimal places it was Y = 0.368 + 0.012T) and the relevant adjusted seasonal index?
Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.
Please do NOT include any units in your answer.


QUESTION 34
If we exponentially smooth the data in Table 1 with a smoothing constant of 0.2, the smoothed value for Quarter 2 in 2005 would be?
Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.
Please do NOT include any units in your answer.


QUESTION 35
If we exponentially smooth the data in Table 1 with a smoothing constant of 0.2, the forecast for Quarter 1 2009 would be?
Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.