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 10. Diane obtains 1000 random samples of size nequals5 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 nequals35 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 left​, but not as much as the original distribution. Jack​'s distribution is expected to be approximately normal. Your answer is correct.B. Jack​'s distribution is expected to be skewed left​, but more than the original distribution. Diane​'s distribution is expected to be approximately normal. C. Diane​'s distribution and Jack​'s distribution are expected to be approximately normal.​ However, Diane​'s will have a greater standard deviation. D. 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) What do you expect the mean of Diane​'s distribution to​ be? What do you expect the mean of Jack​'s distribution to​ be? Diane​'s distribution is expected to have a mean of????. Jack​'s distribution is expected to have a mean of?????

Answer 1

Answer: 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 10. Diane obtains 1000 random samples of size nequals5 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 nequals35 from the population.

Solution:

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.

Diane's obtains 1000 random samples of size n= 5 from the given population. So, sample size n=5, which is small. Therefore, It is skewed right because population is skewed right. But it is not same as population shape.

Jack obtains 1000 random samples of size n= 35 from the given population. So, sample size n= 35, which is large. Therefore, it could expect the sampling distribution of sample mean is bell shaped.

The Option (D) is correct answer.

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) What do you expect the mean of Diane​'s distribution to​ be? What do you expect the mean of Jack​'s distribution to​ be?

The sampling distribution of the sample mean follows normal distribution with mean

μ​​​​​​x = μ

So, from the given information, it could expect both distributions to have a mean of 70.

Diane​'s distribution is expected to have a mean of 70.

Jack​'s distribution is expected to have a mean of 70.