1. Chapter 9 Hypothesis Testing: Single Population
Statistics for
Business and Economics 7th Edition
Chapter 9
Hypothesis Testing:
Single Population
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What is a Hypothesis?
9.1
A hypothesis is a claim
(assumption) about a
population parameter:
population mean
population proportion
Example: The mean monthly cell phone bill of this city is μ = $42
Example: The proportion of adults in this city with cell phones is p = .68
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The Null Hypothesis, H0
States the assumption (numerical) to be tested
Example: The average number of TV sets in U.S. Homes is equal to three ( )
Is always about a population parameter, not about a sample statistic
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The Null Hypothesis, H0
(continued)
Begin with the assumption that the null hypothesis is true
Similar to the notion of innocent until proven guilty
Always contains “=” , “≤” or “” sign
May or may not be rejected
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5. The Alternative Hypothesis, H1
Is the opposite of the null hypothesis
e.g., The average number of TV sets in U.S. homes is not equal to 3 ( H1: μ ≠ 3 )
Never contains the “=” , “≤” or “” sign
May or may not be supported
Is generally the hypothesis that the researcher is trying to support
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6. Hypothesis Testing Process
Claim: the
population
mean age is 50.
(Null Hypothesis:
Population
H0: μ = 50 )
Now select a random sample X Is = 20
likely if μ = 50?
Suppose
the sample
If not likely,
REJECT
mean age
is 20: X = 20
Sample
Null Hypothesis
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7. Level of Significance, 
Defines the unlikely values of the sample statistic if the null hypothesis is true
Defines rejection region of the sampling distribution
Is designated by  , (level of significance)
Typical values are .01, .05, or .10
Is selected by the researcher at the beginning
Provides the critical value(s) of the test
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8. Level of Significance and the Rejection Region
Represents
critical value a a
H0: μ = 3 H1: μ ≠ 3 /2 /2
Rejection region is shaded
Two-tail test
H0: μ ≤ 3 H1: μ > 3 a
Upper-tail test
H0: μ ≥ 3 H1: μ < 3 a
Lower-tail test
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9. Hypothesis Tests for the Mean
 Known
 Unknown
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10. Test of Hypothesis for the Mean (σ Known)
9.2
Convert sample result ( ) to a z value
Hypothesis
Tests for 
σ Known
σ Unknown
Consider the test
The decision rule is:
(Assume the population is normal)
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Decision Rule
H0: μ = μ0
H1: μ > μ0
Alternate rule: a
Do not reject H0
Reject H0 Z zα μ0
Critical value
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12. Example: Upper-Tail Z Test for Mean ( Known)
A phone industry manager thinks that customer monthly cell phone bill have increased, and now average over $52 per month. The company wishes to test this claim. (Assume  = 10 is known)
Form hypothesis test:
H0: μ ≤ the average is not over $52 per month
H1: μ > the average is greater than $52 per month
(i.e., sufficient evidence exists to support the
manager’s claim)
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13. Example: Find Rejection Region
(continued)
Suppose that  = .10 is chosen for this test
Find the rejection region:
Reject H0
 = .10
Do not reject H0
Reject H0
1.28
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14. Example: Sample Results
(continued)
Obtain sample and compute the test statistic
Suppose a sample is taken with the following results: n = 64, x = ( = 10 was assumed known)
Using the sample results,
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Example: Decision
(continued)
Reach a decision and interpret the result:
Reject H0
 = .10
Do not reject H0
Reject H0
1.28
z = 0.88
Do not reject H0 since z = 0.88 < 1.28
i.e.: there is not sufficient evidence that the
mean bill is over $52
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One-Tail Tests
In many cases, the alternative hypothesis focuses on one particular direction
This is an upper-tail test since the alternative hypothesis is focused on the upper tail above the mean of 3
H0: μ ≤ 3
H1: μ > 3
This is a lower-tail test since the alternative hypothesis is focused on the lower tail below the mean of 3
H0: μ ≥ 3
H1: μ < 3
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Upper-Tail Tests
H0: μ ≤ 3
H1: μ > 3
There is only one critical value, since the rejection area is in only one tail a
Do not reject H0
Reject H0 zα Z μ
Critical value
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Lower-Tail Tests
H0: μ ≥ 3
H1: μ < 3
There is only one critical value, since the rejection area is in only one tail a
Reject H0
Do not reject H0
-z Z μ
Critical value
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Two-Tail Tests
In some settings, the alternative hypothesis does not specify a unique direction
H0: μ = 3 H1: μ ¹ 3
/2
/2
There are two critical values, defining the two regions of rejection x 3
Reject H0
Do not reject H0
Reject H0 z
-z/2
+z/2
Lower critical value
Upper
critical value
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