his Question: 12 pts 2of10 (0 complete) 1 This Test: 12 Determine the sample siz

Question

his Question: 12 pts 2of10 (0 complete) 1 This Test: 12 Determine the sample size needed for each of the situations shown below a. N-3,600 b N 5,400 c. N:5,000,000 d. Compare and comment on your answers to parts (a) through (c). 700 = 700 700 196' 50 1960-50 1.960x -50 a n-(Round up to the nearest whole number) b n(Round up to the nearest whole number) c(Round up to the nearest whole number) d. What do the results from parts (a) through (c) show? A. As N increases, the requred sample size n decreases O B. The required sample size n is approximately equal to the square root of N C. As N increases, the required sample size n increases O D. Changing the value of N does not affect the required sample size n.

Explanation / Answer

(a) Here Margin of error = 50 = 1.96 * /n * (N-n)/(N-1)

50 = 1.96 * 700/n * (3600- n)/3599)

2.1863 =  (3600- n)/n

4.78 = (3600 - n)/n

4.78n = 3600 - n

n = 622.85 or 623

(b)

Here Margin of error = 50 = 1.96 * /n * (N-n)/(N-1)

50 = 1.96 * 700/n * (5400- n)/5399)

2.6778 =  (5400- n)/n

7.1704 = (5400 - n)/n

7.1704n = 5400 - n

n = 660.92 or 661

(c)

Here Margin of error = 50 = 1.96 * /n * (N-n)/(N-1)

50 = 1.96 * 700/n * (5000000- n)/4999999)

81.4894 =  (5000000- n)/n

6640.514 = (5000000- n)/n

n = 752.84 or753

(d) Here if there is change in value of N then the required sample increse by increaasing the population size. OPtion C is correct.

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