Question

It has been established that under normal conditions, adults released from drug treatment stay clean for an average period of 12.3 weeks with a standard deviation of 3 weeks. People who have been running a new program, called SUCCESS, claim that their results are better than the average. A research group from the NIJ took a random sample of 100 participants from the SUCCESS program and found the mean of this sample to be 13.4 weeks of sobriety. Which of the following is the most appropriate statistical conclusion?

		The researchers cannot conclude that the program is better than what is normal because 13.4 weeks is less than one standard deviation from the established mean (12.3 weeks) for this type of program.
		The researchers can conclude that the program is better than what is normal because the sample mean should be almost identical to the population mean with a large sample of 100 people.
		The researchers can conclude that the SUCCESS program is better than what is normal because the difference between 12.3 weeks and 13.4 weeks is much larger than the expected sampling error.

Answer 1

given that

mean = 12.3

population standard deviation = 3

sample size n = 100

standard error = standard deviation/sqrt(n)

= 3/sqrt(100)

= 3/10

= 0.30

We can see that the sample mean is more than 3 times of the standard error from the population mean

i.e. 12.3 + 3*0.3 = 13.2 < 13.4 (this is sample mean)

So, we can say that the sample mean is signficantly better than population mean

option C

The researchers can conclude that the SUCCESS program is better than what is normal because the difference between 12.3 weeks and 13.4 weeks is much larger than the expected sampling error.