Math 160 - Cooley Intro to Statistics OCC
Section 12.2 – Hypothesis Tests for One Population Proportion
HYPOTHESIS TEST #5 – The One-Proportion z-Test
Purpose: To perform a hypothesis test for a population proportion, p.
Assumptions:
1) Simple random sample
2) Both np0 and n(1 – p0) are 5 or greater
Step 1 – The null hypothesis is and the alternative hypothesis is one of the following:
/ or / / or /(Two- tailed) / (Left-tailed) / (Right-tailed)
Step 2 – Decide on the significance level a.
Step 3 – Compute the value of the test statistic , and denote that value as z0.
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Math 160 - Cooley Intro to Statistics OCC
Section 12.2 – Hypothesis Tests for One Population Proportion
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Math 160 - Cooley Intro to Statistics OCC
Section 12.2 – Hypothesis Tests for One Population Proportion
CRITICAL VALUE APPROACH
Step 4 – The critical value(s) are
or or .
(Two-tailed) (Left-tailed) (Right-tailed)
Use Table II to find the critical value(s).
Step 5 – If the value of the test statistic falls in the
rejection region, reject H0; otherwise, do
not reject H0.
P-VALUE APPROACH
Step 4 – Use Table II to obtain the P-value.
Step 5 – If , reject H0; otherwise, do not
reject H0.
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Math 160 - Cooley Intro to Statistics OCC
Section 12.2 – Hypothesis Tests for One Population Proportion
Step 6 – Interpret the results of the hypothesis test.
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Math 160 - Cooley Intro to Statistics OCC
Section 12.2 – Hypothesis Tests for One Population Proportion
J Exercises:
1) The number of successes and the sample size are given for a simple random sample from a population. Decide (based off the assumptions needed) whether using the one-proportion z-test is appropriate:
a) , , ,
b) , , ,
2) Christmas Presents. The Arizona Republic conducted a telephone poll of 758 Arizona adults who
celebrate Christmas. The question asked was, “In your family, do you open presents on Christmas Eve
or Christmas Day?” Of those surveyed, 394 said they wait until Christmas Day.
a) Determine the sample proportion.
b) At the 5% significance level, do the data provide sufficient evidence to conclude that a majority
of Arizona families who celebrate Christmas wait until Christmas Day to open their presents?
3) Families in Poverty. In 2000, 8.6% of all U.S. families had incomes below the poverty level, as
reported by the U.S. Census Bureau in Current Population Reports. During that same year, of 400
randomly selected families whose householder had at least a Bachelor’s degree, 9 had incomes below
the poverty level. Do the data provide sufficient evidence to conclude that, in 2000, the percentage of
families that earned incomes below the poverty level was lower among those whose householders had
at least a Bachelor’s degree than among all U.S. families? Use a = 0.01.
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