Question

In a 2008 survey, people were asked their opinions on astrology— whether it was very scientific, somewhat scientific, or not at all scientific. Of 1430 who responded, 76 said astrology was very scientific. B. Find a 95% confidence interval for the population portion with this belief.

Answer 1

Answer:

95% Confidence interval:  (0.0415,0.0647)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1430

Number of people who responded that astrology was very scientific, x = 76

$\hat{p} = \dfrac{x}{n} = \dfrac{76}{1430} = 0.0531$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.0531\pm 1.96(\sqrt{\dfrac{0.0531(1-0.0531)}{1430}})\\\\ = 0.0531\pm 0.0116\\=(0.0415,0.0647)$

95% confidence interval for the population portion with this belief: (0.0415,0.0647)