Question

The Pew Internet and American Life Project reported on the widespread use of the Internet to search for information regarding experimental treatments or medicines. From telephone interviews of 1293 adult Internet users, it was found that 237 had searched for information on experimental treatments or medicines in the past year.

• With 96 % confidence, we estimate between  % and  % of adult Internet users had searched for information on experimental treatments or medicines in the past year. (After converting to percentages, round the limits of your interval to two decimal places.)
• If the study were repeated with a sample of 1687 adult Internet users, what would happen to the margin of error for the interval?
  • the margin of error would decrease
  • the margin of error would not be affected
  • the margin of error would increase
• Based on the interval calculated, could one conclude less than 20% of adult Internet users have searched for information on experimental treatments or medicines in the past year? Explain.
  • Yes because the lower limit of the interval is less than 20%.
  • No because the upper limit of the interval is greater than 20% while the lower limit is less than 20%.
  • Yes because both limits of the interval are below 20%.
  • No because both limits of the interval are below 20%.

Answer 1

Point estimate of the population proportion, p = 237/1293

= 0.1833

Corresponding to 96% confidence, the critical z score = 2.054

Margin of error = = 0.0221

Thus, the 96% confidence interval = (0.1833 - 0.0221, 0.1833 + 0.0221)

= (0.1612, 0.2054)

With 96% confidence, we estimate between 16.12% and 20.54% of adult internet users had searched for information on experimental treatments or medicines in the past year

If the sample size Increases to 1687, the margin of error would decrease

Based on the interval calculated, one cannot conclude that less than 20% of adult internet users have searched for information on experimental treatments or medicines in the past year

No because the upper limit of the interval is greater than 20% while the lower limit is less than 20%