Introduction to Probability and Statistics for Engineers and Scientists

8.4Testing the Equality of Means of Two Normal Populations 317

The value of the t-statistic is −1.898695

The p-value is 0.03607

The p-value of the Two-sample t-Test

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Clear List 2

Clear List 1

One-Sided

Two-Sided

Is greater than

Is less than

Data value = 7

Data value = 6.5

6

7.5

6

7.5

5.5

7

6.5

List 1 Sample size = 10

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List 2 Sample size = 12 8

7.5

6.5

7.5

6

8.5

7

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Is the alternative

hypothesis

Is the alternative

that the mean

of sample 1

?

the mean

of sample 2?

FIGURE 8.6

Of course, if it were not convenient to run Program 8.4.2 then we could have performed
the test by first computing the values of the statisticsX,Y,Sx^2 ,Sy^2 , andSp^2. where theX
sample corresponds to those receiving vitamin C and theY sample to those receiving
a placebo. These computations would give the values

X=6.450, Y=7.125

Sx^2 =.581, Sy^2 =.778

Therefore,

Sp^2 =

9

20

Sx^2 +

11

20

Sy^2 =.689