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 who work a part-time job during the school year is greater than 0.28. The guidance counselor tests the hypotheses H0: p = 0.28 versus Ha: p > 0.28, where p = the true proportion of all high school students who work a part-time job during the school year. The conditions for inference are met. The standardized test statistic is z = 1.89 and the P-value is 0.0294.

What conclusion should be made using the α = 0.05 significance level?

a. Because the P-value is less than α = 0.05, there is convincing evidence that the true proportion of all high school students who work a part-time job during the school year is greater than 0.28.

b. Because the P-value is less than α = 0.05, there is not convincing evidence that the true proportion of all high school students who work a part-time job during the school year is greater than 0.28.

c. Because the P-value is less than α = 0.05, there is convincing evidence that the proportion of high school students in this sample who work a part-time job during the school year is greater than 0.28.

d. Because the P-value is less than α = 0.05, there is not convincing evidence that the proportion of high school students in this sample who work a part-time job during the school year is greater than 0.28.