Section 8-3 Testing a Claim About a Proportion The test statistic is computed by a specific formula depending on the type of the test. The test statistic is a value used in making a decision about the null hypothesis. Typical values used in practice: = 0.1, 0.05, or 0.01 (in percents, 10%, 5%, or 1%).Ģ1 Testing hypothesis Step 1: compute Test Statistic It characterizes the chances that the test fails (i.e., type I error occurs) It must be a small number. of Elementary Statistics, 10th EditionĢ0 Significance Level The probability of the type I error (denoted by ) is also called the significance level of the test. This is a critical error, should be avoided! Type II error: the alternative hypothesis is true, but we reject it => we reject the claim, hence we decline the new medicine and continue using the old one (no harm…).
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Null hypothesis: H0 : p=p0 Alternative hypothesis: H1 : p>p (agrees with the original claim) of Elementary Statistics, 10th Editionġ9 Example (continued) Type I error: the null hypothesis is true, but we reject it => we accept the claim, hence we adopt the new (inefficient, potentially harmful) medicine. Final conclusion would be: for couples using the XSORT the likelihood of having a baby girl is indeed equal to 0.5ġ2 Example 3 Claim: for couples using the XSORT method the likelihood of having a baby girl is at least 0.5 Express this claim in symbolic form: p≥0.5 (again p denotes the proportion of baby girls) Null hypothesis must say “equal to”, so H0 : p=0.5 (this agrees with the claim!) Alternative hypothesis must express difference: H1 : pp0, than the old (existing) one. Final conclusion would be: for couples using the XSORT, the likelihood of having a baby girl is not 0.5 If we fail to reject the null hypothesis, then the original clam is accepted. Final conclusion would be: XSORT method does not increase the likelihood of having a baby girl.ġ0 Example 2 Claim: for couples using the XSORT method the likelihood of having a baby girl is 50% Express this claim in symbolic form: p=0.5 (again p denotes the proportion of baby girls) Null hypothesis must say “equal to”, so H0 : p=0.5 Alternative hypothesis must express difference: H1 : p0.5 Original claim is now the null hypothesisġ1 Example 2 (continued) If we reject the null hypothesis, then the original clam is rejected. If we fail to reject the null hypothesis, then the original clam is rejected. Final conclusion would be: XSORT method increases the likelihood of having a baby girl. If we reject the null hypothesis, then the original clam is accepted. We express this claim in symbolic form: p>0.5 (here p denotes the proportion of baby girls) Null hypothesis must say “equal to”, so H0 : p=0.5 Alternative hypothesis must express difference: H1 : p>0.5 Original claim is now the alternative hypothesisĩ Example 1 (continued) We always test the null hypothesis. The symbolic form of the alternative hypothesis must use one of these symbols: , (not equal, less than, greater than) Give examples of different ways to word “not equal to,”, such as ‘is different from’, ‘fewer than’, ‘more than’, etc.Ĩ Example 1 Claim: the XSORT method of gender selection increases the likelihood of having a baby girl. The alternative hypothesis (denoted by H1) is the statement that the parameter has a value that somehow differs from the null hypothesis. Either reject H0 or fail to reject H (in other words, accept H0 ).
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Introduce the word ‘significant’ in regard to hypothesis testing.Ħ Null Hypothesis: H0 The null hypothesis (denoted by H0) is a statement that the value of a population parameter (such as proportion, mean, or standard deviation) is equal to some claimed value. If, under a given assumption, the probability of a particular observed event is exceptionally small, we conclude that the assumption is probably not correct. If 13 or 14 couples have girls, the method is probably increases the likelihood of a girl.Ĥ Rare Event Rule for Inferential Statistics If 6 or 7 or 8 have girls, the method probably does not increase the likelihood of a girl. This is a claim about proportion (of girls) To test this claim 14 couples (volunteers) were subject to XSORT treatment.
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Population proportion p population mean population standard deviation page 386 of Elementary Statistics, 10th Edition Various examples are provided below definition boxģ Example Claim: the XSORT method of gender selection increases the likelihood of having a baby girl. page 386 of Elementary Statistics, 10th Edition Various examples are provided below definition boxĢ Main Objectives We will study hypothesis testing for A hypothesis test is a standard procedure for testing a claim about a property of a population. 1 Definitions In statistics, a hypothesis is a claim or statement about a property of a population.