Question

4) To estimate the population proportion of a given survey, what sample size would be required if we want a margin of error of 0.045; a confidence level of 95%; and p and q are unknown.

5). How many cars must be randomly selected and tested in order to estimate the mean braking distance of registered cars in the US? We want a 99% confidence that the sample mean is within 2 ft of the population mean, and the population standard deviation is known to be 7 ft.

6) In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Construct a 95% confidence interval estimate of the proportion of all adults who have that belief. Write a statement interpreting the confidence interval.

Answer 1

4)

Here, ME = 0.045
z value at 95% = 1.96
p= 0.5

ME = z *sqrt(p*(1-p)/n)

0.045 = 1.96 *sqrt(0.5 *(1-0.5)/n)
n = ( 1.96/0.045)^2 * 0.5*(1-0.5)
n = 474

5)

ME = 2 , s = 7
z value at 99% = 2.576

ME = z *(s/sqrt(n))
2 = 2.576 *(7/sqrt(n))
n = (2.576 * 7/2)^2
n = 81

6)

p = 589/745 = 0.791

z value at 95% =1.96

CI = p+/- z *sqrt(p*(1-p)/n)
= 0.791 +/- 1.96 *sqrt(0.791*(1-0.791)/745)
= (0.7614 , 0.8198)

we are 95% confident that the proportion of all adults who have that belief. is between (0.7614 , 0.8198)