What Is Business Statistics and Why Does

NAME: ______________________________________
STUDENT NUMBER:__________________________
Math 20000D – Business Statistics
TERM TEST 2: 30 Marks Available (5% of Final Grade) Winter 2020
Instructions:
Unless noted otherwise,
 round all percentages to two decimal places
 round all other figures to at least four decimal places
If your final answer is incorrect you will need to show/explain your work in order to get partial
marks. (Use the space provided. You can use the back of the test sheets also.)
Calculators and Excel are permitted.
Data for test is available on Slate (TERMTESTDATA2)
Copies of Solutions are to be submitted in the dropbox Week 13
Questions start on next page
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1) Hypothesis test (2 sample) (6 marks)
A developer wants to know if the houses in two different neighborhoods were built at roughly
the same time. He takes a random sample of houses from each neighborhood and finds the
summary statistics for the two shown in the table below:
At α=0 . 01 , test the claim that there is no significant difference between the average age of
the houses
Neighborhood Sample mean
x Population standard deviation
σ
Sample size
n
1 57.2 yrs 7.51 yrs 30
2 47.6 yrs 7.85 yrs 35
HINT: use test statistic
z= ( x1−x2 )− ( μ1−μ2 )
√ σ1
2
n1
+ σ 2
2
n2
.
Solution:
Null hypothesis: There is a significant difference between the average ages of the houses.
Alternative hypothesis: There is a significant difference between the average ages of the houses.
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Test statistic (Z) = 5.0313
Alpha = 0.01
P-value = 0.0000
It is clear that P-value < alpha. Hence the null hypothesis is significant. Therefore it may
be summarized that there is a significant difference between the average ages of the houses.
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2) Categorical Data Analysis (6 marks)
A marketing manager at a department stores in Square One would like to know how the last
price reduction campaign affected the customers’ shopping frequency. Data previous showed
 30% of the customers hardly ever shopped at the store,
 20% shopped 1-2 times a year,
 22% shopped 3-4 times a year,
 28% shopped more than 4 times a year.
A random sample of 100 customers was taken two months after the campaign had been
completed. The observed shopping frequencies are in the table below. At 5% significance
level, does it mean that the shopping frequency has significantly changed? Use χ2
distribution.
Shopping
Frequency
Observed
Frequency O
Expected
Frequency E = np O – E (O – E)2 ( O−E ) 2
E
Hardly ever 18
1-2 times a year 22
3-4 times a year 23
More than 4 times a year 37
100 100 χ2=∑ ( O−E ) 2
E =
Null hypothesis: There is no differences between the shopping frequencies.
Alternative hypothesis: There is a difference between the shopping frequencies.
Solution:
Shopping Observed
Frequency
O
Expected
O – E (O – E)2
( O−E ) 2
E
Frequency Frequency E
= np
Hardly ever 18 30 -12 144 4.8
1-2 times a
year 22 20 2 4 0.2
3-4 times a
year 23 22 1 1 0.04545455
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