Economic Statistic Exam Harvard Case Solution & Analysis

Economic Statistic Exam Case Solution

The probability is 0.9649 or 96.49 percent that the number of people that you would have needed to poll in order to be 99% sure that the `yes' side will win the referendum (in other words, so that there is only a 1% chance that `no' will win).

1. The variance of the sample proportion is

V = N * P * Q

V = 500 * 54 % * 46 %

V = 124.2

1. Standard Deviation is

STDEV = V ^ (1/2)

STDEV = 124.2 ^ (1/2)

STDEV = 11.145

Question 3

1. The mean or expected number of interruptions per day is

(0.32 + 0.35 + 0.18 + 0.08 + 0.04 + 0.02 + 0.01) / 7 = 0.1429

1. The standard deviation of expected number of interruptions per day is

((Sum of (x – Mean)²⁾ / (total number of interruptions – 1)) ^(1/2) = 0.01025

1. P (X ≥ 18)

P(X≥ 18) = P (Z ≥ ((18 – 14.29) / 1.025))

P(X≥ 18) = P (Z ≥ 3.62)

P(X≥ 18) = 1 – 0.9998

P(X≥ 18) = 0.0002

The probability is 0.0002 or 0.02 percent that the value of X will be 18 or greater than 18.

1. P(X≥ 17)

P(X≥ 17) = P (Z ≥ ((17 – 14.29) / 1.025))

P(X≥ 17) = P (Z ≥ 2.64)

P(X≥ 17) = 1 – 0.9959

P(X≥ 17) = 0.0041

The probability is 0.0041 or 0.41 percent that the value of X will be 17 or greater than 17.

Question 4

N = 200

Mean = 5

Variance = 10 ^ 2

Standard Deviation = 10

1. P (X ≤ 99)

P(X≤99) = P (Z ≤((99 – 5) / 10))

P(X≤99) = P (Z ≤9.4)

P(X≤99) = 0.9998

1. P (X ≤ 99)

P(X≤99) = P (Z ≤((99 – 5) / 10))

P(X≤99) = P (Z ≤9.4)

P(X≤99) = 0.9998

1. The probability is 0.9998 or 99.98 percent that the confidence interval containing the true mean with a probability of at least 0.99, using the weak law of large numbers (WLLN).
2. The Chebyshev's Theorem is a fact that applies to all possible data sets. It describes the minimum proportion of the measurements that lie must within one, two, or more standard deviations of the mean.
3. For each CLT and WLLN, the rate at which confidence bands become narrower as sample size increases is

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