Question

pose that 5% of the screws a company sells are defective. Figure B.7 shows sample proportions from two sampling dis- tributions: One shows samples of size 100, and the .15 Defective Screws Sup other shows samples of size 1000. (a) What is the center of both distributions? (b) What is the approximate minimum and maxi- mum of each distribution? (c) Give a rough estimate of the standard error in each case. (d) Suppose you take one more sample in each case Would a sample proportion of 0.08 (that is, 8% defective in the sample) be reasonably likely from a sample of size 100? Would it be reason- ably likely from a sample of size 1000? 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Proportion Defective (n 100) 0.00 0.02 0.04 0.06 0.080.10 0.12 Proportion Defective (n 1000) Figure B.7 Sampling distributions for n 100 and n 1000 screws

Answer 1

1) From the graph we can say that the center for both the distributions is approximately same.

The center for both the distributions is 0.05.

2) For a sample of 100 the minimum value is 0.00 and the maximum value is 0.10

For a sample of 1000 the minimum value is 0.03 and the maximum value is 0.07.

3) we know the formula for estimate of standard error

$SE=\sqrt{\frac{p(1-p)}{n}}$

for n=100

$SE=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.05(1-0.05)}{100}}=0.022$

for n=1000

$SE=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.05(1-0.05)}{1000}}=0.007$

d)As the maximum value for n=100 is 0.10, the sample proportion of 0.08 is likely to occur in this distribution ,but in n=1000 the sample proportion of 0.08 is not likely to occur (the maximum proportion in the distribution of n=1000 is 0.07 ).