B) A left tailed test

Reconsider the example of the mean amount of coffee can produced by company. The company claims that these cans, on average, contain 100 grams of coffee. However, if these cans contain less than the claimed amount of coffee, then the company can be accused of cheating. Suppose that the government agency wants to test whether the amount of coffee can is less than 100 grams. Note that the key phrase this time is less than, which indicates a left tailed test. Let be the mean amount of coffee in all cans. The null and alternative hypothesis for this test are written as

(The mean is not less than 120 grams)

(The mean is less than 120 grams)

In this case, we can also write the null hypothesis as . This will not affect the result of the test as long as the sign in is less than.

When the alternative hypothesis has a less than (<) sign, as in this case, the test is always left tailed. In a left tailed test the rejection region is always in the left tail of the distribution curve, as shown in Figure 1.2.

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