Question

research center survey of 427 women showed that 29.0% of them purchased books online. among the 427 women, what is the number of women who said they purchased books online? find a 95% confidence interval esitmate of the percentage of all women who purchased books online.

Answer 1

Yea you asked a relatively highly leveled question not only stats or A.P stats but collaborative stats and I think no one here is at the level for this question. Sorry. Wish you luck.

Answer 2

The number of women in the survey who purchased books online is given by:
\[427\times0.29=124\ (rounded\ up)\]
The survey result forms a binomial distribution where:
n = 427
p = 0.29
(1 - p ) = 0.71
The standard distribution is given by:
\[s.d.=\sqrt{np(1-p)}=\sqrt{427\times0.29\times0.71}=9.377\]
The sample mean is
\[np=427\times0.29=123.83\]
The confidence interval is estimated from:
\[123.83\pm(1.96\times\frac{9.377}{\sqrt{427}})=123.83\pm0.89\]
The percentages of women who purchased books online corresponding to these limit are:
\[\frac{122.94}{427}\times\frac{100}{1}=28.8\ percent\]
and
\[\frac{124.72}{427}\times\frac{100}{1}=29.2\ percent\]