Question

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the past 30 days they had used their phone while in a store to call a friend or family member for advice about a purchase they were considering. The poll surveyed 1007 adults living in the United States by telephone. Of these, 467 responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering. (a) Find ( ±±0.0001) SEpˆSEp^ the sample proportion, the standard error of the sample proportion, and the margin of error for 95% confidence. pˆp^ = SEpˆSEp^ = mm = (b) Find the 95% large-sample confidence interval ( ±±0.001) for the population proportion. the 95% large-sample confidence interval is from to

Answer 1

the sample proportion p^ = 467 / 1007 = 0.4637

the standard error of the sample proportion SE = sqrt(p^(1-p^)/n) = sqrt(0.4637*0.5363/1007) = 0.0157

For 95%, α=0.05 and Zc​=1.96

margin of error for 95% confidence ME = Zc * SE = 1.96 * 0.0157 = 0.0308

95% large-sample confidence interval

p^ +/- ME = (0.4637 +/- 0.0308) = (0.4329, 0.4945)