1. View the video showing sampling from a normal population. In this demonstrati
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1. View the video showing sampling from a normal population. In this demonstration, we took 1000 samples of size 10 from a normal (25, 7) population, measured the mean of each sample and then described the distribution of the 1000 sample means. We found that the means were normal with mean of the means = 24.97 and standard deviation of the means 2.18 means should have a normal shape with When sampling from a normal population, the mean of the means-mean of the population and std. dev. of the means std. dev. of the population square root of sample size. This is explained on p. 353 of the text as well. Given that we sampled from a normal (25, 7) population, theoretically, the means should be normal with mean of the means- std. dev. of the means Why are our actual results,X N(24.97,2.18)), close but not exact? 2. Watch the video showing sampling from a non-normal population (may wish to view the population of rectangles document as well). This population of 100 rectangles is extremely skewed. In the demonstration, we first looked at the distribution of sample means for n-5, then for n-10 and finally for n-30. Eventually, the sample means were approximately normal. In general, what condition would need to be satisfied for the results of Central Limit Theorem ( X ~ M f1,-|) to hold approximately for any population, regardless of its shape? Please note that this is explained on pp. 355-356 of the text as well.Explanation / Answer
(1) mean of means=25 and standard deviation of means=7/sqrt(10)=2.21
Due to sampling fluctuation the sample value may not equal to population value
(B) here the sampling distribution will have
mean=6 and standard deviation of means=2.2/sqrt(20)=0.4919
(C)here the sampling distribution will have
mean=1520and standard deviation of means=770/sqrt(100)=77
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