A researcher interested in the effectiveness of a smoking ce

A researcher interested in the effectiveness of a smoking cessation program does a study in which she measures the number of cigarettes smoked by each person entering the program. Since the number of cigarettes smoked is a \"counting variable\", the population distribution is positively skewed. That is, most people smoke somewhere around 20 or 30 cigarettes a day, but a few people smoke 100 cigarettes or more each day. The population mean number of cigarettes smoked is 27.1 and the population standard deviation is 5.35.
What does the Central Limit Theorem tell us about the distribution of sample means from this population when the sample size is 124?

1-- True False  The distribution of sample means will approximate a normal distribution.
2-- True False  The typical distance between the sample means and the population mean is 0.480.
3-- True False  The mean of the distribution of sample means will be 27.1.
4-- True False  The standard deviation of the distribution of sample means will equal 5.35.

Solution

A researcher interested in the effectiveness of a smoking cessation program does a study in which she measures the number of cigarettes smoked by each person entering the program. Since the number of cigarettes smoked is a \"counting variable\", the population distribution is positively skewed. That is, most people smoke somewhere around 20 or 30 cigarettes a day, but a few people smoke 100 cigarettes or more each day. The population mean number of cigarettes smoked is 27.1 and the population standard deviation is 5.35.
What does the Central Limit Theorem tell us about the distribution of sample means from this population when the sample size is 124?

1-- True False  The distribution of sample means will approximate a normal distribution.

(By Central Limit Theorem)

2-- True False  The typical distance between the sample means and the population mean is 0.480.

3-- True False  The mean of the distribution of sample means will be 27.1.

4-- True False  The standard deviation of the distribution of sample means will equal 5.35

(Sd =5.35/sqrt(124) =0.48)