# MCQs in Statistics

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 35

What is the centred moving average that would correspond to Quarter 4 in 2006? 0.506

Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.

QUESTION 36

What is the adjusted seasonal index for Quarter 4 __________%? 1.350

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.

QUESTION 37
The trend line for this decomposition model can be read off the partial regression printout (at 5 decimal places) to be y = 0.36806 + 0.1195T where T represents Time

Df SS
Regression 1 0.04857
Residual 14 0.00056
Total 15

Coefficients Standard Error
Intercept 0.36806 0.00393
T 0.01195 0.00034

Analysing the partial regression printout, what is the coefficient of determination (r2) for this trend line? (Select the closest correct answer)
a)0.2973
b)0.5452
c)0.7165
d)0.9886

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? 0.656

Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.

QUESTION 39

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? 0.376

Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.

QUESTION 40

If we exponentially smooth the data in Table 1 with a smoothing constant of 0.2, the forecast for Quarter 1 2009 would be? 0.605

Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.

The following information refers to the next question:

The data below represents the amount of grams of carbohydrates in a sample serving of breakfast cereal.

10
18
24
30
19
22
24
20
18
25
20
22
19

QUESTION 16

The variance for this data would be __________ grams. 22.1410

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