A school guidance counselor is concerned that a greater proportion of high school students are working part-time jobs during the school year than a decade ago. A decade ago, 28% of high school students worked a part-time job during the school year. To investigate whether the proportion is greater today, a random sample of 80 high school students is selected. It is discovered that 37.5% of them work part-time jobs during the school year. The guidance counselor would like to know if the data provide convincing evidence that the true proportion of all high school students that work a part- time job during the school year is greater than 0.28. The conditions for inference are met.
What is the value of the test statistic and P-value for this test?
O Z = 0.28 - 0.375 / √0.375(1-0.375) / 80, P-value = 0.0392
O Z = 0.28 - 0.375 / √0.375(1-0.375) / 80, P-value = 0.9608
O Z = 0.375 - 0.28 / √0.28(1-0.28) / 80, P-value = 0.0294
O Z = 0.375 - 0.28 / √0.28(1-0.28) / 80, P-value = 0.9706