Certain lottery claims that 10% of tickets win some prize

Certain lottery claims that 10% of tickets win some prize. Sample of 50 tickets had 3 winners. At .01 level, test claim that proportion is 10%. State hypotheses and identify claim, find critical value(s), compute test value, make decision, summarize results.

Solution: The null and alternative hypotheses are

We use a z-test for proportions. We define. The test statistics is computed as

The critical values at the 0.01 level of significance is. This means that we fail to reject the null hypothesis. In other words, we don’t have enough evidence to claim that the proportion is not 10%.