The Null Hypothesis,Ho continued) Begin with the assumption that the null hypothesis is true Similar to the notion of innocent until proven guilty Refers to the status quo "Always contains“=”,“≤”or“≥”sign May or may not be rejected Statistics for Ma agers Using Microsoft Excel Chap 8-6
Statistics for Managers Using Microsoft Excel Chap 8-6 The Null Hypothesis, H0 Begin with the assumption that the null hypothesis is true Similar to the notion of innocent until proven guilty Refers to the status quo Always contains “=” , “≤” or “” sign May or may not be rejected (continued)
The Alternative Hypothesis,H1 Is the opposite of the null hypothesis e.g.,The average number of TV sets in U.S. homes is not equal to3(H1:μ≠3) Challenges the status quo ·Never contains the“="”,“≤”or"≥”sign May or may not be proven Is generally the hypothesis that the researcher is trying to prove Statistics for Mar agers Using Microsoft Excel Chap 8-7
Statistics for Managers Using Microsoft Excel Chap 8-7 The Alternative Hypothesis, H1 Is the opposite of the null hypothesis e.g., The average number of TV sets in U.S. homes is not equal to 3 ( H1: μ ≠ 3 ) Challenges the status quo Never contains the “=” , “≤” or “” sign May or may not be proven Is generally the hypothesis that the researcher is trying to prove
A Summary of the Null and Alternative Hypothesis The Null Hypothesis Ho,is the hypothesis that is always tested. The Alternative Hypothesis,H1,is set up as the opposite of the null hypothesis and represents the conclusion supported if the null hypothesis is rejected The Null Hypothesis always refers to a specified value of the population parameter (such as u),not to a sample statistic (such as X) Statistics for agers Using Microsoft Excel Chap 8-8
Statistics for Managers Using Microsoft Excel Chap 8-8 A Summary of the Null and Alternative Hypothesis The Null Hypothesis H0, is the hypothesis that is always tested. The Alternative Hypothesis, H1, is set up as the opposite of the null hypothesis and represents the conclusion supported if the null hypothesis is rejected The Null Hypothesis always refers to a specified value of the population parameter (such as u), not to a sample statistic (such as ) X
Hypothesis Testing Process Claim:the population mean age is 50. (Null Hypothesis: Population H0:μ=50) Now select a random sample Is X-20 likely if u 50? If not likely, Suppose 亦亦7 the sample REJECT mean age Sample Null Hypothesis is20:X=20 Statistics for Managers Using Microsoft Excel Chap8-9
Statistics for Managers Using Microsoft Excel Chap 8-9 Population Claim: the population mean age is 50. (Null Hypothesis: REJECT Suppose the sample mean age is 20: X = 20 Sample Null Hypothesis Is 20 likely if μ = 50? Hypothesis Testing Process If not likely, Now select a random sample H0: μ = 50 ) X
Reason for Rejecting Ho Sampling Distribution of X 20 μ=50 If Ho is true If it is unlikely that ..then we we would get a ↑ reject the null sample mean of if in fact this were hypothesis that this value... the population mean... μ=50. Statistics for Ma agers Using Microsoft Excel Chap 8-10
Statistics for Managers Using Microsoft Excel Chap 8-10 Sampling Distribution of X μ = 50 If H0 is true If it is unlikely that we would get a sample mean of this value ... ... then we reject the null hypothesis that μ = 50. Reason for Rejecting H0 20 ... if in fact this were the population mean… X