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STAT 135 LAB 14 TA: Dongmei Li

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Hypothesis Testing Are the results of experimental data due to just random chance? Significance tests try to discover if data can be explained by chance alone.

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Procedure of Hypothesis Testing Step 1: Identify the parameter of interest. Step 2: Specify the null and alternative statements about the parameter. : null hypothesis, what we try to find evidence against. Usually “no effect” or “no difference”. : alternative hypothesis, what we are trying to prove.

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Procedure (continued) Step 3: Does the sample statistic follow the normal curve? – If yes, find the standard score under the null hypothesis. Step 4: Calculate the P-value using Table B. P-value = the probability that the sample outcome would be as extreme or more extreme than the actually observed outcome, given the null hypothesis was true.

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Procedure (continued) Step 5: State the conclusion in terms of the problem If p-value is > 5% Accept the null hypothesis, the observed differences can be explained by chance. If p-value is < 5% Reject the null hypothesis. Results are statistically significant, the observed differences cannot be explained by just chance.

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Lab 14 Question: – Is a person’s ring finger typically longer than their index finger? Step 1: Identify parameter of interest. – : the average difference in length of ring and index fingers Step 2: Specify the null and alternative hypothesis. – : (no difference in length) – : (length of ring finger is typically longer than length of index finger)

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Results We gathered experimental data (i.e. each of you measured the difference in length of ring and index fingers). Sample average = 0.3 Sample standard deviation = 0.18 Sample size = 24

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Learning objective for Lab 14 86. To test Ho: μ = μ 0 versus Ha: μ > μ 0 for a specified value μ 0, and a known standard deviation σ, we can use the test statistic and compute the P- value as the percentage of the normal curve that is above z.

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