Question

stat 250

QUESTION 7 7) Annual report of a certain city noted that normally adults released from drug treatment stay clean for an average period of 13.2 weeks with a standard deviation of 4 weeks. A new program known as PROGRESS claimed that their results are better than the average. A research group from a City Agency took a random sample of 120 participants from the PROGRESS program and found the mean of this sample to be 14.5 weeks of sobriety. Which of the following is the most appropriate statistical conclusion? The researchers can conclude that the PROGRESS program is better than what is normal because the difference between 13.2 weeks and 14.5 weeks is much larger than the expected sampling error. The researchers cannot conclude that the new program is better than what is normal because 14.5 weeks is less than one standard deviation from the established mean (13.2 weeks) for this type of program. The researchers can conclude that the new program is better than what is normal because the sample mean should be almost identical to the population mean with a large sample of 120 people.

Answer 1

Result:

QUESTION 7 7) Annual report of a certain city noted that normally adults released from drug treatment stay clean for an average period of 13.2 weeks with a standard deviation of 4 weeks. A new program known as PROGRESS claimed that their results are better than the average. A research group from a City Agency took a random sample of 120 participants from the PROGRESS program and found the mean of this sample to be 14.5 weeks of sobriety. Which of the following is the most appropriate statistical conclusion?

Sampling error = sd/sqrt(n) = 4/sqrt(120) =0.365148

Mean difference = 14.5-13.2 =1.3

Correct option: The researchers can conclude that the PROGRESS program is better than what is normal because the difference between 13.2 weeks and 14.5 weeks is much larger than the expected sampling error.

The researchers cannot conclude that the new program is better than what is normal because 14.5 weeks is less than one standard deviation from the established mean (13.2 weeks) for this type of program.

The researchers can conclude that the new program is better than what is normal because the sample mean should be almost identical to the population mean with a large sample of 120 people.