reject or fail to reject

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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