Question

A USA Today article claims that the proportion of people who believe global warming is a serious issue is 0.78, but given the number of people you've talked to about this same issue, you believe it is different from 0.78. The hypotheses for this test are Null Hypothesis: p = 0.78, Alternative Hypothesis: p ≠ 0.78. If you randomly sample 23 people and 15 of them believe that global warming is a serious issue, what is your test statistic and p-value?

Answer 1

= 15/23 = 0.652

The test statistic z = ( - p)/sqrt(p(1 - p)/n)

                              = (0.652 - 0.78)/sqrt(0.78 * (1 - 0.78)/23)

                               = -1.48

P-value = 2 * P(Z < -1.48)

              = 2 * 0.0694

              = 0.1388