Question

How did you use your cell phone? 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 1003 adults living in the United States by telephone. Of these, 462 responded that they had used thier 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) Report the sample proportion, the standard error of the sample proportion, and the margin of error for 95% confidence.

b) Are the guidelines for when to use the large-sample confidence interval for a population proportion satisfied in this setting? Explain your answer.

c) Find the 95% large-sample confidence interval for the population proportion.

d) Write a short statement explaining the meaning of your confidence interval.

Answer 1

a) = 462/1003 = 0.4606

SE = sqrt((1 - )/n)

     = sqrt(0.4606 * (1 - 0.4606)/1003)

     = 0.0157

At 95% confidence interval the critical value is z_0.025 = 1.96

Margin of error = z_0.025 * SE

                         = 1.96 * 0.0157

                         = 0.0308

b) Yes, the the guidelines are satisfied to use the large-sample confidence interval. Because the sample size is very large and each trials are independent, so that we can use normal approximation.

c) The 95% confidence interval for population proportion is

+/- SE

= 0.4606 +/- 0.0157

= 0.4449, 0.4763

d) We are 95% confident that the true population proportion lies in the above interval.