is a statement regarding a characteristic of one or more populations.
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Hypothesis Testing
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a procedure, based on sample evidence and probability, used to test statements regarding a characteristic of one or more populations.
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Null Hypothesis
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denoted H0 (Red "H-naught"), is a statement to be tested. The null hypothesis is a statement of no change, no effect, or no difference and is assumed true until evidence indicates otherwise.
In hypothesis​ testing, the null hypothesis is a statement of no​ change, no​ effect, or no difference and it is denoted Upper H0. The alternative hypothesis is a statement we are trying to find evidence to support and it is denoted Upper H1.
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Alternative Hypothesis
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denoted H1 (read "H-one"), is a statement that we are trying to find evidence to support.
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One-Tailed Test
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Left and right tailed tests
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If we reject the null hypothesis when the statement in the null hypothesis is​ true, we have made a Type I error.
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A Type I error occurs if the null hypothesis is rejected​ when, in​ fact, the null hypothesis is true. A Type II error occurs if the null hypothesis is not rejected​ when, in​ fact, the alternative hypothesis is true.
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If we do not reject the null hypothesis when the statement in the alternative hypothesis is​ true, we have made a Type​ II error.
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A Type I error occurs if the null hypothesis is rejected​ when, in​ fact, the null hypothesis is true. A Type II error occurs if the null hypothesis is not rejected​ when, in​ fact, the alternative hypothesis is true.
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Sample evidence can prove that a null hypothesis is true.
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The correct answer is False because although sample data is used to test the null​ hypothesis, it cannot be stated with​ 100% certainty that the null hypothesis is true. It can only be determined whether the sample data supports or does not support the null hypothesis.
Try Again
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Four Outcomes from Hypothesis Testing
Three years​ ago, the mean price of a​ single-family home was ​$243 comma 795243,795. A real estate broker believes that the mean price has decreased since then.
Type I Error: The broker rejects the hypothesis that the mean price is ​$243,795​, when it is the true mean cost.
Type I Error: The sample evidence led the researcher to believe the standard deviation of monthly cell phone bills is different from ​$49.61​, when in fact the standard deviation of bills is ​$49.61.
Type II Error: The broker fails to reject the hypothesis that the mean price is ​$243,795, when the true mean price is less than ​$243,795.
Type II Error: The sample evidence did not lead the researcher to believe the standard deviation of monthly cell phone bills is different from ​$49.61​, when in fact the standard deviation of bills is different from $49.61.
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1. Reject the null hypothesis when the alternative hypothesis is true. This decision would be correct.
2. Do not reject the null hypothesis when the null hypothesis is true. This decision would be correct.
3. Reject the null hypothesis when the null hypothesis is true. This decision would be incorrect. This type of error is called a Type I error.
4. Do not reject the null hypothesis when the alternative hypothesis is true. This decision would be incorrect. This type of error is called Type II error.
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Tailed Test Results
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If a hypothesis test has an equal hypothesis versus a not equal​ hypothesis, then it is a​ two-tailed test.
If it has an equal hypothesis versus a less than​ hypothesis, then it is a​ left-tailed test.​
Finally, if it has an equal hypothesis versus a greater than​ hypothesis, then it is a​ right-tailed test.
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What happens to the probability of making a Type II​ error, betaβ​, as the level of​ significance, alphaα​, ​decreases? Why?
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As the level of​ significance, alphaα​, ​decreases, the probability of making a Type II​ error, betaβ​, increases. As we decrease the probability of rejecting a true null​ hypothesis, we increase the probability of not rejecting the null hypothesis when the alternative hypothesis is true.
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