Question

In 2012, the percent of American adults who owned cell phones and used their cell phones to send or receive text messages was at an all-time high of 80%. Assume that 80% refers to the population parameter. More recently in 2015, a polling firm contacts a simple random sample of 110 people chosen from the population of cell phone owners to confirm the percent who use their phone to text. The firm askes each person "do you use your cell phone to send or receive texts Yes or No. "

a) Verify that the conditions are met so that the central limit theorem can apply to p̂

b) What is the approximate distribution of p̂, the proportion of cell phone owners in the 2015 sample who use their cell phone to text? Give the shape, mean, and standard deviation.

c) What is the probability that p̂ is between 78% and 82%: what is P(0.78 < p̂ < 0.82). In other words, what is the probability that p̂ estimates π within 2% of 0.8?

d) Suppose the polling firm increased the number of people in its sample to 1100 people. Now what is the probability that p̂ is between 78% and 82%? In other words, what is the probability that p̂ estimates π within 2%?

e) Which sample size (110 or 1100) gives a more accurate estimate of the population proportion of cell users who text?

Answer 1