 # Economic Statistic Exam Case Solution & Answer

## Economic Statistic Exam Case Solution

### Question 1:

1. The mean is 2.1 and the variance is 1.655
 Percentages Treatments Mean 1-P Variance 55% 1 0.55 45% 0.2475 15% 2 0.3 85% 0.255 10% 3 0.3 90% 0.27 10% 4 0.4 90% 0.36 5% 5 0.25 95% 0.2375 5% 6 0.3 95% 0.285 2.1 1.655

1. Mean = 2.1

Standard Deviation = (1.655) ^ (1/2)

 Percentages Treatments Mean 1-P Variance 20% 1 0.2 80% 0.16 30% 2 0.6 70% 0.42 25% 3 0.75 75% 0.5625 15% 4 0.6 85% 0.51 10% 5 0.5 90% 0.45 2.65 2.1025

Mean = 2.65

Standard Deviation = (2.1025) ^ (1/2)

T = (Mean 1 – Mean 2) / ((V1 / N1) + (V2 / N2)) ^ (1/2)

T = 0.67

P = 1 – 0.2598

P = 0.7402

The probability is 0.7402 or 74.02 percent that the randomly-selected patient will be cured more quickly (i.e. will require fewer doses) with the new treatment.

1. Mean = 2.1

Standard Deviation = (1.655) ^ (1/2)

Mean = 2.65

Standard Deviation = (2.1025) ^ (1/2)

T = (Mean 1 – Mean 2) / ((V1 / N1) + (V2 / N2)) ^ (1/2)

T = 0.67

P = 0.2598

The probability is 0.2598 or 25.98 percent that the randomly-selected patient will be cured at a lower cost with the new treatment.

1. Mean = 2.1

Standard Deviation = (1.655) ^ (1/2)

80 % Probability = 3 doses

P (X ≥ 80)

P(X≥ 80) = P (Z ≥ ((3 – 2.1) / (1.655) ^ (1/2)))

P(X≥ 80) = P (Z ≥ 0.7)

P(X≥ 80) = 1 – 0.2576

P(X≥ 80) = 0.7424

The probability is 0.7424 or 74.24 percent that the value of X will be 80 or greater than 80.

1. 95 % Confidence interval is

Standard Deviation = (1.655) ^ (1/2)

Mean = 2.1

N = 200

Mean = 2.65

Standard Deviation = (2.1025) ^ (1/2)

N = 250

A 95 percent level of confidence has α = 0.05 and critical value of zα/2 = 1.96.

Confidence Interval = 2.65± 1.96 * ((2.1025) ^ (1/2)/ 250)

Lower Limit = 2.638632

Upper Limit = 2.661368

Confidence Interval = 2.1 ± 1.96 * ((1.655) ^ (1/2) / 200)

Lower Limit =2.087392613

Upper Limit = 2.112607387

Lower limit Difference = 2.638632 – 2.087392613 = 0.551239387

Upper Limit difference = 2.661368 – 2.112607387 = 0.548760613

### Question 2

N = 500

P = 54 %

Q = 1 – 54 % = 46 %

1. P(X46)

P(X46) = P (Z ((46 – 54) / 24.84))

P(X46) = P (Z – 0.322)

P(X46) = 0.3745

The probability is 0.3745 or 37.45 percent that the majority of the population plans to vote ‘no’.

N = 500

P = 54 %

Q = 1 – 54 % = 46 %

1. P(X54)

P(X54) = P (Z ((54 – 54) / 24.84))

P(X54) = P (Z 0)

P(X54) = 0.5

The probability is 0.5 or 50 percent that the majority of the population plans to vote ‘yes’.

N = 500

P = 54 %

Q = 1 – 54 % = 46 %

1. P(X99)

P(X99) = P (Z ((99 – 54) / 24.84))

P(X99) = P (Z 1.81)

P(X99) = 0.9649……………………

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