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Chapter 2: Frequency Distributions
Chapter Outline
2.1 Introduction to Frequency Distributions
2.2 Frequency Distribution Tables
Obtaining
Tutorial 10 solutions
Regression solutions 39 40
Question 39.
(a) There appears to be a positive linear relationship. There is also considerable random variation
around the values on the line of best fit, but the R2 value indicates that nearly 80% of the
Tutorial 8 solutions
Solutions to tutorial questions 32 34
32. Let be the population mean annual income.
(a) We are asked to see if we can prove that the management negotiator is correct, so we
are looking for strong evidence that the mean annual income f
Tutorial 9 solutions
Solutions to tutorial questions 35 38
35. Limits of 95% confidence interval:
14.9
s
x t 2
= 156.3 t0.025
12
n
where the critical value of t is taken from the distribution with 11 degrees of freedom.
t0.025 = 2.201 . Therefore Confiden
Solutions to tutorial questions 28 31
28.
Let X be the random variable length of component. Then X ~ N (117,2.1) .
(units of cm)
X 117 120 117
3
(i) Pr( X 120) Pr(
) Pr(Z
)
2.1
2.1
2.1
where Z is a standard normal random variable.
3
Pr(Z
) Pr(Z 1.43) 1
22
(a)
Probabiity distribution for number of absences
0.3
0.25
Probability
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
Number absent
Bar chart used, since this is a quantitative discrete variable.
As well as being used for qualitative data, a bar chart is used fo
Solutions to tutorial problems 17-21: Probability
17. (a)
(i)
Table of probabilities obtained by dividing through by
2000:
W
W
R
(ii)
0.21
0.14
0.57
0.08
R
Including marginal probabilities (row and column totals.)
W
R
0.21
0.14
0.57
0.08
Total
0.78
0.22
T
Tutorial 3 solutions questions 15 16
15. Note that in this ogive, the classes are 14 24, 24 34, etc.
Ogive of age distribution of divorced people in Australia, 1997
and 2001
percentage of divorced persons
who are under the age specified
on the x axis
100
41. For the following graphs of time series, comment on what components appear to be
present. Is it possible to decide if the components should be combined additively or
multiplicatively?
Price of winter coats
Price of winter coats in
Ruritania ($)
(a)
Ti
44. Two forecasting procedures were applied to the series in Excel Ex34 in order to forecast
the sales for the four quarters of 2006. The forecasts and the actual sales are given in
the following table (sales and forecasts in $million):
Year
2006
Quarter
35. Selvanathan et al., p.450, 11.37.
You are given the following statistics: x 156.3, s 14.9, n 12 .
Estimate the population mean with 95% confidence.
What assumption must be made to answer this question?
36. (Selvanathan question 11.42 page 451)
A parki
32. During Enterprise Bargaining negotiations between management and unions, the
management negotiator argues that the companys building workers who are paid an
average of $50,000 per year, are well paid because the mean annual income of all
building work
15. The ogive shows the percentage of divorced persons who are younger than the age
specified on the x axis, for 1997 and 2001. Note: the class boundaries are 14, 24, 34
etc.
(a) Interpret the fact that the 2001 ogive is to the right of the 1997 ogive.
(b
28. Selvanathan et al., p.405, 10.14.
An automatic machine in a manufacturing process is operating properly if the lengths of
an important subcomponent are normally distributed, with mean = 117 cm and
standard deviation = 2.1 cm.
If the machine is operati
25. (a) Use Table 1 in Section 10 of this Unit Guide, to find the following probabilities:
(i)
(ii)
(iii)
P(Z 0.4)
P(Z <1.52)
P(Z 1.94)
(iv)
(v)
(vi)
P(Z 1.96)
P(Z >1.96)
P(0 < Z <1.28)
(b) Use Table 1 in Section 10 of this Unit Guide to find the value z*
22. The manager of manufacturing at the Afford Motor Company is concerned about the
absenteeism of assembly line employees. Using historical data, he obtained the
following probability distribution of X, the number of assembly line employees absent on
any
17. The owner of an appliance store is interested in the relationship between the price at
which an item is sold (retail price or sale price) and the customers decision on whether
or not to purchase an extended warranty for the item. The owner has constru
12. A survey of the number of non-family employees of 132 small businesses in the town of
Shallowhaven yields the following results:
Number of employees
0
1
2
3
4
5
Frequency
35
31
33
13
17
3
(a) For this sample data obtain:
(i)
(ii)
(iii)
the mean
the me
Questions 8 - 11
8.
Suppose that n = 3, x1 = 5, x2 = 8, x3 = 14, y1 = 7, y2 = 3 and y3 = 8.
Evaluate the following:
3
(a)
3
(b)
xi
i 1
(d)
i 1
3
3
(xi 9)
(e)
i 1
(g)
i 1
xi yi
i 1
(xi 9)
2
(f)
i 1
3
x
i
i 1
2
2
3
3
(c)
yi
xi2
(h)
n
n
2
xi xi
i 1
Exercise 31: Regression using Excel
Adapted from Selvanathan et al., Exercise 14.20. Data in Exercise31_33.xls
See section 7.5.3 of this unit guide for instructions on how to use the Regression tool in
Excel. This will be used in exercises 31, 32 and 33.