math QAs

Two sample hypothesis tests

The procedure for testing two samples in Minitab Express is similar to the procedure for testing one

sample, but there are some differences…

t-test: Two Independent Samples

Example 1: A university professor suspects that the time a class meets could affect how students learn, so

she takes a sample of test scores for 20 students from a large 8am

statistics class and an equally large 2pm statistics class. A

summary of the sample data is given below.

n x s

8am class 20 73.2 9.6

2pm class 20 79.1 11.2

Click the Statistics tab and select Two Samples.

Since the 2 samples are independent, select this option

A dialog box like the one

shown here will open. Since

we have the summary of

data in this example, select

Summarized data.

The dialog box will change

appearance.

Enter the summary data for the two samples

Click the Options tab.

Select the appropriate alternative hypothesis

Leave this box unchecked!

We will never assume equal variances!

Click OK.

The results will appear in the output window

Summary statistics

Confidence interval for the difference

Results of the hypothesis test

Including the p-value

Example 2: Big Foods Grocery has two grocery stores located in Johnston City.

One store is located on First Street and the other on Main Street and each is run by

a different manager. Do customers at the Main Street store spend more that the First

Street store? The following table shows the sample data collected from the two

stores.

In this example, the data values are given, so enter these data into Minitab Express.

Click the Statistics tab and select Two Samples.

Since the 2 samples are independent, select this option

A dialog box like the one

shown here will open.

Since we have the data

values in 2 columns

select Each sample is in

its own column

The dialog box will change appearance. Now, select the 2

columns in which the sample data are located.

Click the options tab.

Select the appropriate alternative hypothesis

(in this case, we suspect that the mean of the First

Street store is less than the Main Street store, so the

difference: First minus Main would be less than 0)

Again, leave this box unchecked!

Click OK

In addition to the summary statistics, confidence interval,

and other information, the output window will contain the

results of the hypothesis test:

First Street

Main Street

15.78 15.19

17.73 18.22

10.61 15.38

15.79 15.96

14.22 21.92

13.82 12.87

13.45 12.47

12.86 13.96

10.82 13.79

12.85 13.74

18.4

18.57

17.79

10.83

t-test: Two Dependent Samples

Example 3: Forty-four sixth graders were randomly selected from a school

district. Then, they were divided into 22 matched pairs, each pair having equal

IQ's. One member of each pair was randomly selected to receive special

training. Then, all of the students were given an IQ test. Test results are

summarized at right. Did the training help or hurt student performance? This is

an example of a matched-pairs or dependent samples test.

Click the Statistics tab and select Two Samples.

Since the 2 samples are dependent, select this

option (paired t)

Select the columns containing the data

for the 2 samples.

Be sure to select

the appropriate

alternative

hypothesis from

the Options tab

The output looks like this:

Pair Training No

training

1 95 90

2 89 85

3 76 73

4 92 90

5 91 90

6 53 53

7 67 68

8 88 90

9 75 78

10 85 89

11 90 95

12 85 83

13 87 83

14 85 83

15 85 82

16 68 65

17 81 79

18 84 83

19 71 60

20 46 47

21 75 77

22 80 83

Test for 2 proportions

Example 4: In a recent survey of drinking laws, a random sample of 900 women showed that 585 were in

favor of increasing the legal drinking age. In a random sample of 850 men, 510 favored increasing the

legal drinking age. Test the hypothesis that the percentage of men and women

favoring a higher legal drinking age is the same.

Click the Statistics tab and select Two Samples.

Since we want to compare two proportions, select Proportions

We have the summary data, so in

the pull-down menu, select

Summarized data.

Enter the data for each sample.

Note: Number of events is the

same as the number of successes

(x). Number of trials is the total number in the sample (n)

Click the Options tab.

Select the appropriate alternative hypothesis

In the Test method: menu, select Use the pooled

estimate of the proportion.

Press OK.

The output looks like this:

Sample statistics

The p-value (use the Normal

Approximation value) = 0.0308

So at the 0.05 level, you reject the null hypothesis and conclude that the percentage of men and women

who favor a higher legal drinking age is significantly different.