Example 6: Suppose a political poll estimates that 60% of all Canadian adults (21 years or older) favour capital punishment. From this information, can you determine the exact proportion of all Canadian adults that favour capital punishment? Explain.
The
Math 1213 Assignment 5 Solutions [84 marks]
8A1. [12]
a) The equation of the least squares line is y = 1049.50 0.415119x.
b) RSquared, or the coefficient of determination equals .968. This indicates that the least
squares line has a strong fit to this da
Elementary Statistics for Business and Behavioural Sciences 1
MATH 1213

Spring 2016
Sampling Distribution Models
Sampling Proportion pp = y / n = pq/n where q = 1 p cfw_sampling distributions are a displays of
summary statistics (phats) for many different samples dont say sample distribution when you mean
SAMPLING distribution We use pq/
Elementary Statistics for Business and Behavioural Sciences 1
MATH 1213

Spring 2016
Inferences about Means
The tdistribution is the zdistribution but for samples. Depends on n to determine shape. Generally
unimodal and symmetrical around the mean (like the normal distribution). However, tdistributions are
flatter and become flatter (t
Elementary Statistics for Business and Behavioural Sciences 1
MATH 1213

Spring 2016
Comparing Means
Comparing 2 INDEPENDENT Samples (The two groups we are comparing MUST be independent of each
other. In addition to the independence assumption/randomization condition (within each group), the
normal population assumption (for both groups).
Elementary Statistics for Business and Behavioural Sciences 1
MATH 1213

Spring 2016
Chi Square Goodness of Fit Test:
Count data on one categorical variable, and we want to test whether or not its distribution fits some
hypothetical one (a theory of what the proportions in each category should be).
Example:
Suppose we sample 300 consumers
Math 1213 Assignment 3 Solutions [58 marks]
4A1. a) [1] x =
x
n
i
= (86 + 65 + 80 + 82 + 86 + 68 + 81 + 80 + 67 + 66)/10 = 76.1.
b) [2] Order them: 65, 66, 67, 68, 80, 80, 81, 82, 86, 86
There are ten values, so the median is the average of the middle two
Math 1213 Assignment 6 Solutions [44 marks]
9A14. [8]
a)
A: Aware of the Promotion
N: Not Aware
P: Purchased the
Product
100
25
125
D: Did not purchase the
product
300
75
375
400
100
500
b)1) P(P or A) = P(P) + P(A) P(P and A) = 125/500 + 400/500 100/500
Math 1213 Assignment 4 Solutions [64 marks]
7A1. a) [2] The sample is already ordered from smallest to largest.
AP(P20) = (20/100)n = (.2)(60) = 12
AP(P20) is a whole number, so Pos(P20) = AP(P20) + .5 = 12.5.
P20 is the average of the values in positions
Math 1213 Assignment 7 Solutions [52 marks]
9A32. [8] Let A be the event that someone in this population has AIDS.
Let B be the event that a positive test result is obtained.
P(A) = .006. P(BA) = .98. P( B  A ) = .93. Find P(AB).
P(B  A) P(A)
Bayes Ru
Math 1213 Assignment 9 Solutions
12A1.i)
a) zo = 2.65.
b) P(Z 2.05) = 0.9798 and P(Z 2.06) = 0.9803, so zo 2.05.
c) 1 P(Z zo) = 0.88, so P(Z zo) = 0.12. P(Z 1.18) = 0.1190 and P(Z 1.17) =
0.1210. Since these probabilities are equally distant from 0.12,
Math 1213 Assignment 8 Solutions [48 marks]
11A1. [10]
a) P(Z 1.76) = 0.9608. The students standard normal curves (drawn by hand)
should look like this:
b) Since this distribution is continuous, P(Z < 1.76) = P(Z 1.76) = 0.9608.
c) P(Z > 2.34) = 1 P(Z 2
Example 2 (stopw.mtw): Consider the stopwatch data in example 1 above.
For this sample, (1) Ordered sample: 2 12 16 18 22; n = 5 (2) AP(m) = (.50)n = (3) Pos(m) = (4) m = Interpretation: Approximately 50% of the failure times in the sample fall below m =
INTRODUCTION STATISTICS deals with the collection description interpretation
of DATA. Data may arise naturally as observations of "things as they are", or as a result of a controlled or designed experiment.
The collection of data must be done carefully an
Elementary Statistics for Business and Behavioural Sciences 1
MATH 1213

Spring 2016
When to use What?
Probability Qs. ex: P(ybar > 100) z = ybar / SD(ybar) which is o/square root of n. Z score find pvalue. Subtract 1
pvalue (depends).
Ts and standard error when we do not know SD.
One Sample ttest: A one sample t test is used to exami