Worksheet #12

STA 291-301

Winter 09/10

Hypothesis Testing Procedure (P-Value Method)

Step 1: State the hypotheses.

Step 2: Compute the proper test statistic.

Step 3: Use the test statistic to find the p-value (remember to look at the alternative hypothesis to see if you have a left tailed test, right tailed test, or two tailed test).

Step 4: Make the decision to reject or to not reject the null hypothesis based on whether the p-value is smaller than your level of significance.

Step 5: Summarize the results.

Hypothesis Testing Procedure (Rejection Region Method)

Step 1: State the hypotheses.

Step 2: Choose proper test statistic.

Step 3: Use the critical value (Zα for one tailed test, Zα/2 for two tailed test) to set up the rejection region (left tailed test, right tailed test, or two tailed test).

Step 4: Compute the proper test statistic.

Step 5: Make the decision to reject or to not reject the null hypothesis based on whether the test statistic falls into the rejection region.

Step 6: Summarize the results.

Hypothesis Test Procedure (Confidence Interval Method)

Note: Must be testing equal to, not equal to hypotheses

Step 1: State the hypotheses.

Step 2: Calculate the proper confidence interval.

Step 3: Make the decision to reject or to not reject the null hypothesis based on whether the µ0 (the value we are testing against) falls into the confidence interval.

Step 4: Summarize the results.

Test StatisticsConfidence Intervals for two populations (µ1-µ2 & p1-p2) and Dependent Samples

Examples

Between Wendy’s and McDonald’s, which fast-food drive thru is faster? To answer this question, random samples of service times for each restaurant are measured. A sample of 213 Wendy’s reveals a mean of 149.85 seconds with a standard deviation of 21.82 seconds. A sample of 202 McDonald’s reveals a mean of 154.53 with a standard deviation of 23.64. Test the claim that the two restaurants have the same drive thru service time. Use the confidence interval method.

An insurance company is thinking about offering discounts on its life insurance policies to nonsmokers. As part of its analysis, the company randomly selects 200 men who are 60 years old and ask them if they smoke at least one pack of cigarettes per day and if they have ever suffered from heart disease. 10 out of the 38 smokers had suffered from some type of heart disease and 12 out of 150 nonsmokers had suffered from some type of heart disease. Can we conclude at the 10% level of significance that smokers have a higher incidence of heart disease than nonsmokers? Use the P-value method.

A psychologist has performed the following experiment. For each of 10 sets of identical twins who were born 30 years ago, he recorded their annual incomes, according to which twin was born first. The results (in $1000s) are shown below. Can he infer at α=.05 there is a difference in income between the twins? Use the rejection region method.

Twin Set / First Born / Second Born
1 / 32 / 44
2 / 36 / 43
3 / 21 / 28
4 / 30 / 39
5 / 49 / 51
6 / 27 / 25
7 / 39 / 32
8 / 38 / 42
9 / 56 / 64
10 / 44 / 44