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# Hypothesis Testing of Single Mean and Single Proportion: Decision and Conclusion

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A systematic way to make a decision of whether to reject or not reject the null hypothesis is to compare the p-value and a preconceived αα (also called a "significance level"). A preconceived αα is the probability of a Type I error (rejecting the null hypothesis when the null hypothesis is true). It may or may not be given to you at the beginning of the problem.

When you make a decision to reject or not reject HoHo, do as follows:

• If α>p-valueα>p-value, reject HoHo. The results of the sample data are significant. There is sufficient evidence to conclude that HoHo is an incorrect belief and that the alternative hypothesis, HaHa, may be correct.
• If αp-valueαp-value, do not reject HoHo. The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis, HaHa, may be correct.
• When you "do not reject HoHo", it does not mean that you should believe that HoHo is true. It simply means that the sample data has failed to provide sufficient evidence to cast serious doubt about the truthfulness of HoHo.

Conclusion: After you make your decision, write a thoughtful conclusion about the hypotheses in terms of the given problem.

## Glossary

Hypothesis:
A statement about the value of a population parameter. In case of two hypotheses, the statement assumed to be true is called null hypothesis (notation H0H0 size 12{H rSub { size 8{0} } } {}) and contradictory statement is called alternate hypothesis (notation HaHa size 12{H rSub { size 8{a} } } {}).
p-value:
The probability that event will happen purely by chance assuming the null hypothesis is true. The smaller p-value, the stronger the evidence is against the null hypothesis.
Type 1 Error:
The decision is to reject Null hypothesis, when, in fact, Null hypothesis is true.

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