9.6. Tests about a Population Mean: Small Sample Case

General Case: as and level of significance

.

(I): vs.

Then,

In addition,

.

(II): vs.

In addition,

.

(III): vs.

Then,

In addition,

Example 5:

A sample of 6 observations, 18, 20, 16, 19, 17, 18, is taken.

Suppose the population is normally distributed. Then,

(a) for the hypothesis,

using , test the hypothesis based on the classical hypothesis test?

(b) for the hypothesis,

using , test the hypothesis based on p-value?

(c) for the hypothesis,

using , test the hypothesis based on the confidence interval approach?

[solutions:]

.

(a)

(b)

(c) A 95% confidence interval for is

Since , we do not reject .

JavaStatSoft:

T test:

Statistics -> Tests -> One Sample -> Mean -> T Test