Suppose Diane and Jack are each attempting to use a simulation to describe the s

Question

Suppose Diane and Jack are each attempting to use a simulation to describe the sampling distribution from a population that is skewed left with mean 70 and standard deviation 5. Diane obtains 1000 random samples of size n = 5 from the population, finds the mean of the means, and determines the standard deviation of the means. Jack does the same simulation, but obtains 1000 random samples of size n = 40 from the population. Complete parts (a) through (c) below. (a) Describe the shape you expect for Diane's distribution of sample means. Describe the shape you expect for Jack's distribution of sample means. Choose the correct answer below. A. Diane's distribution is expected to be skewed right, but not as much as the original distribution. Jack's distribution is expected to be approximately normal. B. Diane's distribution is expected to be skewed left, but not as much as the original distribution. Jack's distribution is expected to be approximately normal. C. Jack's distribution is expected to be skewed left, but more than the original distribution. Diane's distribution is expected to be approximately normal. D. Diane's distribution and Jack's distribution are expected to be approximately normal. However, Diane's will have a greater standard deviation. (b) What do you expect the mean of Diane's distribution to be? What do you expect the mean of Jack's distribution to be? A. Diane's distribution is expected to have a mean of 31.3. Jack's distribution is expected to have a mean of 70. B. Diane's distribution is expected to have a mean of 31.3. Jack's distribution is expected to have a mean of 11.1. C. Both Diane's distribution and Jack's distribution are expected to have a mean of 70. D. Diane's distribution is expected to have a mean of 70. Jack's distribution is expected to have a mean of 11.1. (c) What do you expect the standard deviation of Diane's distribution to be? What do you expect the standard deviation of Jack's distribution to be? A. Both Diane's distribution and Jack's distribution are expected to have a standard deviation of 5. B. Diane's distribution is expected to have a standard deviation of 5. Jack's distribution is expected to have a standard deviation of 0.8. C. Diane's distribution is expected to have a standard deviation of 2.2. Jack's distribution is expected to have a standard deviation of 0.8. D. Diane's distribution is expected to have a standard deviation of 2.2. Jack's distribution is expected to have a standard deviation of 5.

Explanation / Answer

a) from central limit theorum ; option B is correct

b) option C is correct

c) for std deviation =population std deviation/(n)1/2

hence option C is correct

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