What is the best way to solve the question of both part a and b? Are there rules

Question

What is the best way to solve the question of both part a and b?

Are there rules I can follow them?

Part I: Each of the following histograms represents a sampling distribution of the sample mean for various sample sizes. Samples of size 5, 20, 50 and 200 were taken from a population that is extremely skewed right. Match each histogram to the appropriate sample size (look carefully at the spread of the histograms!). (2 points each) (Put the numbers5, 2050,200 where they belong) a. 50 700- 6001b 5005 400 30043 2002 100 100 5 50 5 6.0 657.07580 Sample Mean, - S.4 7.2 8.1 9.9 Sample Mean t00 600 500 300 100 100 3.6 547.2 9.0 10.8 12.6 25. 76 6.006.246.436. Sample Mearn Sample Mean b. Based on the sampling distributions above, what do you believe the population mean is? (2 points) The population mean is

Explanation / Answer

(a) As the sample size increases, by the central limit theorem, the sample mean approaches the population mean.

Here very clearly the 2nd and the 4th figure are distributed closely around a value of 6, although figure 2 has some values on top which is equal to 6 but not exactly at 6. Hence that would be sample size 50. Figure 4 has a perfectly normal distribution shape, based on the large sample size.

Now the first and 3rd figures. The 3rd figure is definitely skewed to the right (it has a tail to its right, and that happens because of a very small sample size. Figure 1 too has a skew ness but is ver small compared to fig 3. Therefore figure 1 has n = 20, and figure 3 has n = 5

(b) As stated above, for very large sample sized, (normally > 30) the population mean is equal to the sample mean, for normal distributions. The best is to look at which figure has sample sizes > 30, and look at the cebtral value, and that would be your mean.

Hope this helps.

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