9.5. Two-Tailed Tests about a Population Mean: Large Sample Case

General Case: as and level of significance

vs.

As is known, let

.

As is unknown,

.

Then,

In addition,

reject .

Interval estimation and hypothesis testing

Let vs.

Step 1: Construct a confidence interval

As is known,

As is unknown,

Step 2: If falls into the above confidence intervals, then

do not reject . Otherwise, reject .

Example 4:

A sample of 49 provides a sample mean of 38 and a sample standard deviation of 7.

Let . Please test the hypothesis

.

based on

(a) classical hypothesis test

(b) p-value

(c) confidence interval.

[solution:]

.

(a)

we reject .

(b)

we reject .

(c)

confidence interval is

.

Since , we reject .

JavaStatSoft:

Z test:

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