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.

0H

aH

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)

0H 0aH 0

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 14

• 86. To test Ho: μ = μ0 versus Ha: μ > μ0 for a specified value μ0, 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.