Question

1. A state employment agency has discovered that by eliminating one item from an employment questionnaire, the questionnaire can be completed in a much shorter period of time. That’s good – so long as the shortened time doesn’t affect the results of the questionnaire, which is the number of hours the individual reports to have looked for work in the last 7 days.
   
   To investigate this, the agency asked 76 clients to take a month’s questionnaire twice, telling them that their responses had been “lost by the system” the first time through. In fact, one time the client took the shortened questionnaire and the other time the client took the longer version. For each of the 76 chosen for the study, the researchers calculated the time the clients reported as looking for work, which averaged 17.0 hours based on the long questionnaire. The standard deviation for that data set was 6.1. They also calculated the average of the times that were reported using the shorter form: that average was 17.4 hours with a standard deviation of 6.0.

When the state employment agency calculated the results of the state-wide survey, which was done using the traditional long form, they found that the state wide average that month was 17.1 hours with a standard deviation of 5.9. What can you say – with 95% confidence -- about the reliability of the survey? Would you deem the shortened form an acceptable alternative to the long form?

Answer 1

since the mean :=17 and standard deviation =6.1 of the long form, and we want to compare the survey results with the long form population results. so following would be the way the answer this question

here we want to test the

null hypothesis H0:=17 and

alternate hypothesis Ha:<17,

here we use z-test and z=(-)/=(17.1-17)/6.1=0.016

the one tailed critical z(0.05)=1.645 is more than calculated z=0.016 so we fail to reject H0 and conclude that it deems the shortened form an acceptable alternative to the long form.