C) A right tailed test

Suppose that mean monthly income of all households was 45 500 tg in 2001. We want to test if current income of all households is higher than 45 500 tg. The key phrase in this case is higher than, which indicates a right tailed test.

Let be the mean income of all households.

We write the null and alternative hypothesis for this test as

(The current income is not higher than 45 500 tg)

(The current income is higher than 45 500 tg)

In this case, we can also write the null hypothesis as , which states that current mean income is either equal to or less than 45 500 tg. Again, the result of the test will not be affected whether we use an equal to (=) or a less or equal to () sign in as long as the alternative hypothesis has a greater than (>) sign.

When an alternative hypothesis has a greater than (>) sign, the test is always right tailed. As shown in the Fig. 1.3, in a right tailed test, the rejection region is in the right tail of the distribution curve. The area of this rejection region is equal to , the significance level. We will reject if the value of obtained from the sample falls in the rejection region. Otherwise, we will not reject .

Remark: Note that the null hypothesis always has an equal to (=) or a less or equal to or a greater than or equal to sign and the alternative hypothesis always has a not equal to or a greater than (>) or a less than (<) sign.

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