8 One investigator takes a sample of 100 men age 1824 in a c

8. One investigator takes a sample of 100 men age 18-24 in a certain town. Another takes a sample of 1,000 such men. (a) Which investigator will get a bigger average for the heights of the men in (b) Which investigator will get a bigger SD for the heights of the men in his (c) Which investigator is likely to get the tallest of the sample men? or are the (d) Which investigator is likely to get the shortest of the sample men? or are his sample? or should the averages be about the same? sample? or should the SDs be about the same? chances about the same for both investigators? the chances about the same for both investigators?

Solution

Answer for a)

For a bigger samples Sample average converge to Population mean as per Law of Large Numbers (LLN)

Hence we cant say which sample will get bigger average but the sample mean for 1000 men would be approximately equal to population mean hence Smalle sample\'s average will be bigger

Answer for b)

As small sample sizes give higher SD and as sample size increases SD decreases hence samll sample will have higher SD

Answer for c)

As sample size increases it increases the collectin of all possible outcomes hence bigger size would help to get the tallest of the sample men. AN investigator with 1000 sample size.

Answer for d)

As sample size increases it increases the collectin of all possible outcomes hence bigger size would help to get the shortest of the sample men. AN investigator with 1000 sample size