As a pollster, you randomly called 845 voters to know their positions on a California State’s ballot proposition. Only 80% of th
e voters agreed to answer your questions. Of those who answered you, 386 voters favored the proposition. (a)[2] Explain why this situation should not be considered as the finite population case. (b)[2] Check if the sampling distribution of the sample proportion can be approximately Normal. (c)[3] Construct the 92% CI for the favor proportion π. Sketch the CI. State if π can be 0.52. (d)[3] Construct the 96% CI for the favor proportion π. Sketch the CI. State if π can be 0.55. Hint: Round off probabilities and values to 5 decimal places. Refer to some Excel value lookups:
1 answer:
Step-by-step explanation:
(a)
This is not finite population case because 845 shows the random sample not population.
(b)
Here we have
n = 845 *0.80 = 676 and x=386
Since number of successes (that is 386) and number of failures (that is 290) both are greater than 5 so normal distribution can be assumed.
(c)
[Find solution in the attachment 1]
We cannot conclude that population proportion is 0.52 because it is not in the confidence interval.
(d)
[Find the solution in the attachment 2]
We cannot conclude that population proportion is 0.55 because it is in the confidence interval.
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Answer:
Step-by-step explanation:
We have that the focus is at (p,0) and that the directrix is x=-p. Take the point (-p,0) of the directrix. We know that the vertex of the parabola is at the middle point ot the line segment that joins the points (p,0) and (-p,0). To get the middle piont, we take the average coordinate by coordinate. That is, the middle point is . The general formula of a parabola of vertex (h,k) that opens to the right or to the left is given by
Where |p| is the distance from the focus to the vertex. If the parabola opens to the right, then p>0 and p<0 otherwise. In our case, h =0=k, so we get that