Question

A marketing manager for a cell phone company claims that less than 58% of children aged 8-12 have cell phones. In a survey of 822 children aged 8-12 by a national consumers group, 460 of them had cell phones. Can you conclude that the manager's claim is true? Use the α=0.10level of significance and the critical value method with the table.

Answer 1

We want to test the null hypothesis that the proportion of children aged 8-12 who have cell phones is 0.58, against the alternative hypothesis that the proportion is less than 0.58.

The sample proportion is:

p = 460/822 = 0.559

The sample size is n = 822.

Under the null hypothesis, the test statistic follows a standard normal distribution. The test statistic is:

z = (p - P0)/sqrt(P0(1 - P0)/n)

where P0 is the hypothesized proportion under the null hypothesis.

Substituting the values we obtained, we get:

z = (0.559 - 0.58)/sqrt(0.58(1 - 0.58)/822) = -1.691

The critical value for a one-tailed test with a significance level of 0.10 and 821 degrees of freedom is -1.282. Since the test statistic (-1.691) is less than the critical value (-1.282), we reject the null hypothesis.

Therefore, we can conclude that there is sufficient evidence to support the claim that less than 58% of children aged 8-12 have cell phones.

Hope that is what you are looking for :).