Question

A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book. Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books.

Answer 1

Answer: $(0.10\ ,\ 0.18)$

Step-by-step explanation:

According to the empirical rule, the 95% confidence interval for the true population proportion is given by :-

$(p'-2\sigma_{p'}\ ,\ p'+2\sigma_{p'})$

Given : . The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book.

Then, the 95% confidence interval for the true proportion of adults who prefer e-books will be :-

$(0.14-2(0.02)\ ,\ 0.14+2(0.02))\\\\=(0.14-0.04\ ,\ 0.14+0.04)\\\\=(0.10\ ,\ 0.18)$

Hence, the 95% confidence interval for the true proportion of adults who prefer e-books= $(0.10\ ,\ 0.18)$