Question

5. For the multiple choice questions, circle the best answer.For which of the following situations would the Rule for Sample Means not apply?A. A random sample of size 50 is drawn from a bell-shaped population.B. A random sample of size 20 is drawn from a skewed population.C. A random sample of size 50 is drawn from a skewed population.D. A random sample of size 20 is drawn from a bell-shaped population.Which one of the following statements is false?A. The sampling distribution of the sample mean is exactly normal if the observations are normallydistributed.B. The standard deviation of the sample mean decreases as the sample size increases.C. The sampling distribution of the sample mean becomes approximately normal for large samplesizes.D. The sampling distribution of any statistic becomes approximately normal for large samplesizes.

Answer 1

5i) Option D) is correct

A random sample of size 20 is drawn from a bell-shaped population is correct

ii) Option D) is correct

"The sampling distribution of any statistic becomes approximately normal for large sample sizes is correct"

Explanation:

5 i) The rule for Sample Means not apply is the option D) "A random sample of size 20 is drawn from a bell-shaped population is correct"

For : The population of measurements of interest is bell-shaped,

or A large sample should have atleast of sample size 30 is taken.

In the option we have only sample size 20 so the rules can not applied.

Therefore option D) is correct

ii) The statement false is "The sampling distribution of any statistic becomes approximately normal for large sample sizes is correct"

For : The sampling distribution of a statistic is the distribution of values taken by the statistic in ALL possible samples of the same size from the same population. Not larger or smaller sample

Therefore option D) is correct