Question

As a pollster, you randomly called 845 voters to know their positions on a California State’s ballot proposition. Only 80% of the 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:

Answer 1

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.