![]() Test Statistic for Testing a Claim About a Proportion Note: p is the assumed proportion not the sample proportion. 3) The conditions np 5 and nq 5 are both satisfied, so the binomial distribution of sample proportions can be approximated by a normal distribution with µ = np and = npq. 2) The conditions for a binomial distribution are satisfied. Requirements for Testing Claims About a Population Proportion p 1) The sample observations are a simple random sample. Notation n = number of trials x p = n (sample proportion) p = population proportion (must be specified in the null hypothesis) The test statistic is computed by a specific formula depending on the type of the test. Testing hypothesis Step 1: compute Test Statistic The test statistic is a value used in making a decision about the null hypothesis. It characterizes the chances that the test fails (i.e., type I error occurs) It must be a small number. Significance Level The probability of the type I error (denoted by ) is also called the significance level of the test. 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…). This is a critical error, should be avoided! Null hypothesis:Īlternative hypothesis: H1 : p>p0 (agrees with the original claim)Įxample (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 0.5 11Įxample 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: 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. H1 : p0.5 Original claim is now the null hypothesis 10Įxample 2 (continued) If we reject the null hypothesis, then the original clam is rejected. 9Įxample 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 Final conclusion would be: XSORT method does not increase the likelihood of having a baby girl. 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. H1 : p>0.5 Original claim is now the alternative hypothesis 8Įxample 1 (continued) We always test the null hypothesis. ![]() H0 : p=0.5 Alternative hypothesis must express difference: 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 (not equal, less than, greater than) 7Įxample 1 Claim: the XSORT method of gender selection increases the likelihood of having a baby girl. The symbolic form of the alternative hypothesis must use one of these symbols: .The alternative hypothesis (denoted by H1) is the statement that the parameter has a value that somehow differs from the null hypothesis.Įither reject H0 or fail to reject H0 (in other words, accept 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. ![]() Rare Event Rule for Inferential Statistics 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. ![]() 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. population standard deviation Įxample Claim: the XSORT method of gender selection increases the likelihood of having a baby girl. Main Objectives We will study hypothesis testing for 1. A hypothesis test is a standard procedure for testing a claim about a property of a population. Definitions In statistics, a hypothesis is a claim or statement about a property of a population.
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