Question

A poll of 2,054 randomly selected adults showed that 89% of them own cell phones. The technology display below results from a test of the claim that 94% of adults own cell phones. Use the normal distribution as an approximation to the binomial distribution, and assume a 0.01 significance level . The alternative hypothesis is to show that the population proportion π is not equal to 0.94 a. Is the test two-tailed, left-tailed, or right-tailed? Right tailed test Two-tailed test Left-tailed test b. What is the test statistic? The test statistic is (Round to two decimal places as needed.) c. What is the p-value? The p-value is (Round to three decimal places as needed.)

Answer 1

The test is a two-tailed test because the alternative hypothesis does not specify the direction of the difference. The test statistic and p-value can't be determined without specific numerical values from the question.

Step-by-step explanation:

To address the student's question, we should clarify the nature of hypothesis testing and statistical significance concepts. For part a, given that the alternative hypothesis is to show that the population proportion π is not equal to 0.94, the test is a two-tailed test. This is because the alternative hypothesis does not specify a direction of the difference; it only suggests the proportion is different from 0.94.

For part b, the test statistic can be calculated by using the formula z = (p - p0)/(sqrt(p0(1 - p0)/n)), where p is the sample proportion, p0 is the claimed population proportion and n is the sample size. Since the specific number is not given, an exact test statistic cannot be determined without such data.

Regarding part c, the p-value assesses the strength of the evidence against the null hypothesis. It can be obtained from the standard normal distribution given the calculated test statistic. As with the test statistic, the p-value can't be determined without the exact test statistic value.