Sango Stats
Hypothesis Testing [Critical Value Method]
Claim about a single proportion
Basic Steps of Hypothesis Testing
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Identify the claim
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Write out the hypothesis and label the original claim and counter claim
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Left tail, Right tail, or Two tailed test?
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Identify the critical Z value
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Calculate the test statistic
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Decide – Reject or Fail to Reject the Null Hypothesis
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Conclude – Tie it back to the original claim
Example: Wizard Professor Allen is conducting research on the effectiveness of green magic stones. He studied 200 stones and found that 146 of the stones were effective in producing fire breathing hamsters. He claims that less than 75% of all green stones are effective in producing fire breathing hamsters. Test his claim using a 0.05 level of significance.
1. Identify the claim
75% of all green stones are effective in producing fire breathing hamsters
2. Write out the hypothesis and label the original claim and counter claim
3. Left tail, Right tail, or Two tailed test?
Left Tail
4. Identify the critical Z value
-1.645
p-hat is calculated by dividing x by the sample size (n). 146/200 = 0.73
5. Calculate the test statistic
6. Decide
Fail to reject the Null Hypothesis because the test statistics does not fall inside the rejection zone
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7. Conclude
There is not sufficient evidence to support the claim that less than 75% of all green stones are effective in producing fire breathing hamsters