# Statistical help 1題 ...

Question 6:

(a)

In order to maintain the quality standard, HKBU wants to estimate the proportion of mistakes which its staff members make with a 98% chance that the error of the estimate is less than 6%. How large should the sample size be for such estimation? (5 marks)

(c)

The HKSAR government wants to estimate the percentage of Hong Kong citizens who are willing to pay for mandatory medical insurance. In a survey among 200 citizens, 65 of them are willing to pay. Construct a 90% confidence interval for the proportion of Hong Kong citizens who are willing to pay for mandatory medical insurance. (Correct your answer to 4 decimal places) (5 marks)

### 2 個解答

• 最佳解答

(a)

1-α= 0.98

α= 0.02

α/2 = 0.01

n = (Z 0.01)^2 * pq / e^2

p = q = 1/2 時, pq最大 , 此時

n

= (Z 0.01)^2 * (1/2)(1/2) / e^2

= 2.326^2 * 0.25 / 0.06^2

≒ 375.7

為使誤差小,需保守估計,取376

Ans: 376

(c)

1-α= 0.9

α= 0.1

α/2 = 0.05

p = 65/200 = 0.325

q = 1-p = 1-0.325 = 0.675

所求信賴區間

= 0.325± Z 0.05√(0.325*0.675/200)

≒ 0.325± 1.645*0.033119

≒ 0.2705 ~ 0.3795

Ans: ( 0.2705 , 0.3795 )

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