stat 121 credit quiz 14 a

True or False: Suppose we take all possible samples of the same size from a population and for each sample, we compute x̄. The mean of these x̄ values will be exactly equal to the mean of the population (μ) from which the samples were taken.

TRUE

The following scenario applies to questions 1-4: A population is known to have a Normal distribution with a mean of 180 and a standard deviation of 36 Suppose that all possible samples of size 20 were taken. What would be the mean of the sampling distribution of x̄ ?

180

What will be the standard deviation of the sampling distribution of x̄ if samples of size 20 are taken?

8.05

Suppose we took samples of size 40 instead of 18. What will be the shape of the sampling distribution of x̄

Approximately Normal

Can we compute the probability that x̄ is less than 29 for n=18?

No, because the population is not Normally distributed and we cannot apply the Central Limit Theorem

The following scenario applies to questions 5-7: Suppose we have a left-skewed population distribution with a mean of 30 and a standard deviation of 3. For random samples of size 18, what will be the shape of the sampling distribution of x̄?

Not approximately normal - the Central Limit Theorem does not apply

If all possible samples of size 80 are taken instead of size 20, how would this change the mean and standard deviation of the sampling distribution of x̄?

The mean would stay the same and the standard deviation would decrease

Assume the population is right-skewed. Experiment with various sample sizes of your choosing. What happens to the shape of the sample as the sample size increases?

The sample becomes more and more like the population distribution.

Assume the population is still right-skewed. What happens to the shape of the sampling distribution of x-bar as the sample size increases?

The sampling distribution of x-bar becomes approximately normal.

What will be the shape of the sampling distribution of x̄ if all samples of size 20 were taken?

normal