Answer:
a) Standard deviation of the percentage who will be found by the survey to be very interested (SD) = p(1-p) = 0.88*0.12 = 0.1056
b) By this we mean the margin of error (E) = ± 0.0415
c) Expected number of people = npq = 235*0.88 = 206.8 => 207 people
d) Expected percentage as being very interest = 0.88*207 = 182.16 = 182 people
Step-by-step explanation:
a) By standard deviation in proportion terms, we mean:
==> σ = p(1-p). That is the product of the proportion of those being very interested and those otherwise. And since we know the proportion of those very interested to be 0.88. Then q = 1-p => 1 -0.88 = 0.12 not very interested.
Hence, σ = p(1-p) = 0.88*0.12 = 0.1056.
b) The uncertainty is the margin of error (E) = ± Z*[tex]\sqrt{\frac{p(1-p)}{n} }[/tex], we assumed 95% confidence level and the Z value = 1.96.
Therefore, E = ± 1.96 * [tex]\sqrt{0.1056/235}[/tex] = ± 0.04154838 which we approximated as ± 0.0415.
c) The expected number = np, where n - sample size and p is the proportion of those very interested - since that was the interest in this question.
Therefore,
E(p) = 235*0.88 = 206.8 = 207 people.
d) Expected percentage as being very interest => The percentage of those very interested multiply by the total number of those expected to be very interested.
And this is: 0.88*207 = 182.16 = 182 people
