If the sample size is n = 100, the sampling distribution of the mean will be nor

Question

If the sample size is n = 100, the sampling distribution of the mean will be normally distributed A. only if the individual elements in the underlying parent population are small. B. only if the standard deviation of the mean is normally distributed C. only if the underlying parent population itself is normally distributed D. only if the mean is normally distributed. E. regardless of the shape of the underlying parent population. When applied to the sampling distribution of the mean, the central limit theorem. A. allows us to assume that samples are being drawn from a normal distribution. B. does not need to be invoked when the underlying parent population is known to normal distributed. C. allows us to assume that the sampling distribution is large for all known values of n. D. is applied only if the mean is normally distributed. E. suggests that the smaller n is, the more normal the sampling distribution of means become For large simple random samples drawn from any population, the mean of the sampling distribution sample means is: A. smaller than the mean of the underlying parent population. B. larger than the mean of the underlying parent population. C. equal to the mean of the underlying parent population. D. not related to the value of the mean of the underlying parent population. E. equal to the standard deviation of the underlying parent population.

Explanation / Answer

16. n=100 is fairly large for convergence to a normal distribution. Thus Central Limit Theorem(CLT) can be applied and hence the distribution of the mean will be normal regardless of the shape of the parent population(E).

17. The principal assumption of Central limit theorem is that the underlying sample is large enough. At the same time, it does not need to be invoked when the underlying population is normally distributed. Thus option (B) is correct.

18. When the underlying sample is fairly large, then the mean of the sample converges to the mean of the parent population. Thus option (C) is correct.

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