(b) Thus, you will have the most conservative margin of error when p = 0.5 At least, how many people do you need to survey in order for the most conservative margin of error to become 0.05? Use 1.96 for the critical value of the margin of error.

3. Now, you are now hired as a survey designer. The goal of the survey is to predict the proportion of people in Santa Barbara who support for subsidies for income loss due to CDVID 19. Let p denote the proportion of people who support for the introduction of the subsidies. [lpt.] {a} Show that when p = 0.5, p[1 - p} is the largest compared to other p. [4pt.] Hint: Since p} = p p} is a concave function, p} is the largest at p\" such eel _ that a