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. Define “d” as the difference between the number of hours each individual reported in the two times he/she took the survey (once the long for and the other the short form). For example, John reported 16 hours in the long survey and 18 hours when he took the short survey. His “d” is 2 hours. The average of the 76 differences in the study was 0.5 hours with a standard error of 0.5. 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? (Hint: Although the sample size is relatively large, this is an example of paired samples.)

Answer 1

The value of mean difference average is 0.5 and standard error is also 0.5. therefore

t=(0.5)/(0.5)

i.e t=1

The tabulated value for t test for 75 degrees of freedom is 1.99. which is greater than calculated t value. So hypothesis is accepted i.e shortened form acceptable alternative.