Testing a Claim about a Difference between Proportions — Unit test
Question 8 • AQR_A_IC
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.
Answer
A
If the true proportion of high school students who work a part-time job during the school year is p = 0.747, there is a 0.59 probability that the guidance counselor will find convincing evidence for Ha: p > 0.28.
B
If the true proportion of high school students who work a part-time job during the school year is p = 0.747, there is a 0.59 probability that the guidance counselor will find convincing evidence for Ha: p = 0.28.
C
If the true proportion of high school students who work a part-time job during the school year is p = 0.28, there is a 0.41 probability that the guidance counselor will find convincing evidence for Ha: p > 0.28.
D
If the true proportion of high school students who work a part-time job during the school year is p = 0.28, there is a 0.41 probability that the guidance counselor will find convincing evidence for Ha: p = 0.28.