STAT 135 LAB 14 TA: Dongmei Li

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.

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.

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.

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.

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)

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

Learning objective for Lab 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.