The reasons given in the survey why shoppers purchase on

Question

Assignment: EXCEL Problem Set

Problem 1 - Find the LCM of:

(a) 24, 60, 144

(b) 7, 14, 35, 49

(c) 100, 150, 250

Problem 2 - Evaluate:

(a) 25/7 x 12/5 x 28/3

(b) 5/14 x 36/25 ÷ 6/7

(c) 1.08 x 0.03

Problem 3 - Evaluate

(a) 3³ x 9^-2 x 2²

(b) 5^-2 x 4^-3 x 20²

(c) 3√(250) x 10^2/3 x 6√(256)

Problem 4 - The seasonally adjusted percentage of the population aged over 15 looking for full-time work in the eight Februarys in Australia between February 2005 and February 2012 is sahown in the table below.

Month	Percentage
February 2005	5.1
February 2006	4.9
February 2007	4.4
February 2008	3.4
February 2009	5.3
February 2010	5.5
February 2011	5.0
February 2012	5.2

Source: Australian Bureau of Statistics, Labour Force Australia, Cat. No. 1350.0, Table 8, April 2012.

(a) Illustrate the data using a line chart where the vertical axis starts at 3.0 and ends at 5.5.

(b) What impression does the line chart in (a) give about the percentage of the population aged over 15 looking for full-time work in Australia during February of these years? Do you think it is fair impression of the data? Explain. Also comment on any trend that you notice.

Problem 5 - In a report based on 984 shoppers around the country, the Radio Marketing Bureau found that around 54% of Australians prefer to shop alone, while females and people aged under 45 are more likely to impulse-buy than the rest of the community are.

The reasons given in the survey why shoppers purchase on impulse, along with the percentage in each category, are shown in the following table.

Reason	Percentage
Item on special	35
Noticed item	20
New product	13
No reason	9
Item on display	8
Other	15
Total	100

Illustrate the data using a pie chart.

Problem 6 - The production of beer in megalitres in Australia is shown in the following table for each of the June quarters in the years 2003 to 2010.

Year	Beer production in Australia (MI)
2003	380
2004	390
2005	403
2006	386
2007	383
2008	390
2009	398
2010	374

Source: Australian Bureau of Statistics, Manufacturing Production, June quarters, Cat. No. 8301.0.55.0001

For these data, find:

(a) the range

(b) the mean

(c) the mean deviation

(d) the standard deviation

(e) the coefficient of variation

Problem 7 - In a random sample of 50 subjects, the average person (while sleeping) rolled over a mean of 12 times per night with a standard deviation of 3 times.

(a) Find a 99% confidence interval for the mean number of times the average person rolls over per night while sleeping.

(b) Considering your interval in (at would you believe that the population mean could be 14 times per night? Explain.

Problem 8 - The number of female employees in Australia with leaver entitlements in shown in the following table (in '000) for each for years 1992 and 2007.

Age (years)	1992 (x)	2007 (y)
15-19	266.1	354.3
20-24	463.5	523.0
25-29	421.5	505.3
30-34	419.2	482.7
35-39	441.6	539.2
40-44	446.1	553.6
45-49	364.3	588.9
50-54	225.7	500.9
55-59	130.9	375.4
60-64	44.8	191.7
65+	24.4	77.7
Total	3248.0	4692.5

 Source: Australian Bureau of Statistics, Australian Labour Market Statistics, Cat. No.  6105.0.

(a) Draw a scatter diagram of the data. Comment on the shape.

(b) Calculate the correlation coefficient between the figures for 1992 and 2007.  (Hint: S_xx = 277 335.7, S_yy = 264 062.5 and S_xy = 238 684.8).

(c) Test the value found in (b) for significance. What conclusion can you draw?

Textbook - Croucher,  Introductory Mathematics and Statistics, 6th Ed. (and 6th Ed. Revised).