Advanced Data Analysis – Hypothesis
Testing
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Hypothesis Tests
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z-test
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Used to test hypotheses that a mean is greater (less)
than or equal to some value
For example -- Do ISU students, on average, run 3
miles per day?
Marketing 444 students conducted a simple random
sample on campus, n=100
Advanced Data Analysis – Hypothesis
Testing
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Steps in Hypothesis Testing
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State Null and alternative hypotheses (Null always
means no relationship – reject it if you can)
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Specify the level of statistical significance (a)
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Ho: m = 3
Ha: m ≠ 3
This is 1 - Confidence Interval
Most often .05 (in Marketing Research)
Specify the critical region to be used
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Areas of rejection (of Ho) and cannot reject (of Ho)
Advanced Data Analysis – Hypothesis
Testing
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Collect data and determine test statistic
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For example
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n = 100 (with SRS)
mean = 3.2
s = 1.0
Test hypothesis -- reject or retain the null
hypothesis
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Compute z
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Where z = computed mean – m/sx
computed z ≥ 1.96
Advanced Data Analysis – Hypothesis
Testing
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What if:
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n = 100 (with SRS)
Mean = 3.4
s = 4.0
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n = 500
Mean = 3.4
s = 4.0
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Importance of n and s
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Advanced Data Analysis – Hypothesis
Testing
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Laczniak Yogurt Company is interested in determining and
comparing customer’s attitudes toward its main product in the
southern versus northern region of the country. To make this
determination, data were gathered from 81 customers in the
south and 125 customers in the north.
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The hypothesis is that attitudes among northern customers are
more favorable, because Laczniak Co. is located in New London,
WI, and typically sponsors activities in the northern tier of states.
Advanced Data Analysis – Hypothesis
Testing
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The following data were obtained on a 1 (bad) to 7
(excellent) scale:
South
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North
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M1 = 5.20
s1 = 2.50
State Null and alternative hypotheses (Null always means
no relationship – reject it if you can)
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M2 = 4.64
s2 = 3.00
Ho: m1  m2
Ha: m1 > m2
Compute Z
Test  |Z| ≥ 1.96
Advanced Data Analysis – Hypothesis
Testing
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What if sample size in both were 144?
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What if s in both = 1.00?