## Economic Statistic Exam Case Solution

### Question 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 |

- 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.

- 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.

- 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.

- 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 z_{α/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 %

*P*(*X**≤*46)

*P*(*X**≤*46) = P (Z *≤*((46 – 54) / 24.84))

*P*(*X**≤*46) = P (Z *≤*– 0.322)

*P*(*X**≤*46) = 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 %

*P*(*X**≤*54)

*P*(*X**≤*54) = P (Z *≤*((54 – 54) / 24.84))

*P*(*X**≤*54) = P (Z *≤*0)

*P*(*X**≤*54) = 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 %

*P*(*X**≤*99)

*P*(*X**≤*99) = P (Z *≤*((99 – 54) / 24.84))

*P*(*X**≤*99) = P (Z *≤*1.81)

*P*(*X**≤*99) = 0.9649……………………

This is just a sample partial case solution. Please place the order on the website to order your own originally done case solution.