Research has shown that losing even one night of sleep can have a significant effect on performance of complex tasks such as problem solving Linde Bergstroem 1992 To demonstrate this phenomenon a researcher conducted the following simulated experiment A sample of n 32 college students was given a problem solving task at noon on one day and again at noon on the following day The students were not permitted any sleep between the two tests For each student the difference between the first and second score was recorded For this sample the students averaged Mp 5 7 points better on the first test with a standard deviation of SD 9 6 for the difference scores Conduct an analysis with this data using a 0 01 Put in 1 alpha for the C Level in your calculator Give the 99 confidence interval for the average difference score Round to 3 decimal places