The document provides examples of hypothesis testing procedures for claims about population proportions and means. The first example tests a claim about improving chances of a boy being born and finds the results support the claim. The second example tests a claim about the mean age of graduate students and finds the results do not reject the claim. Both examples relate their conclusions back to whether the results support or do not reject the original claim.

1. Decision 𝑹𝑹𝑹𝑹𝑹𝑹 𝑯 𝟎 𝑭𝑭𝑭𝑭 𝒕𝒕 𝑹𝑹𝑹𝑹𝑹𝑹 𝑯 𝟎
Reason 𝑃 < 𝛼 𝑃 > 𝛼
Conclusion The results of the sample
data support 𝐻 𝑎 and reject
𝐻0
The results of the sample data
do not support 𝐻 𝑎 and do not
reject 𝐻0
Example 1: It’s a Boy Genetics Labs claim their procedures improve the chances of a boy
being born. The results for a test of a single population proportion are as follows:
𝐻0: 𝑝 = 0.5
𝐻 𝑎: 𝑝 > 0.5
𝛼 = 0.01
𝑃 = 0.023
Decision: Since 𝑃 < 𝛼 we reject the null hypothesis
Conclusion: The results of the sample data support the claim that It’s a Boy Genetics Labs
improve the chances of a boy being born at the 0.01 level of significance.
Example 2: The mean age of graduate students at PC University is claimed to be 30 years.
The results of a test of a single population mean are as follows:
𝐻0: 𝜇 = 30
𝐻 𝑎: 𝜇 ≠ 30
𝛼 = 0.05
𝑃 = 0.11
Decision: Since 𝑃 > 𝛼 we fail to reject the null hypothesis
Conclusion: The results of the sample data do not reject the claim that the mean age of
graduate students at PCU is 30 years at the 0.05 level of significance.
Note: Notice how we always relate our conclusion back to the claim whether it is the null or
alternative. In most cases the claim will be the alternative.
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