Question

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?

Answer 1

Solution :-

Givan that ,

= 13.2

= 14.5

= 4

n = 120

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :   = 13.2

Ha : < 13.2

Test statistic = z

= ( - ) / / n

= ( 14.5 - 13.2 ) / 4 / 120

= 3.56

The test statistic = 3.56

P - value = P ( Z < 3.56 ) = 0.9998

P-value = 0.9998

= 0.05  

0.9998 > 0.05

P-value >

Fail to reject the null hypothesis .

There is insufficient evidence to the test claim