We are trying to estimate the average number of hours of sleep per patient in a population of 500 patients all treated with a new type of sleeping pill. The number of hours of sleep during a night recording was observed in 50 patients (randomly selected from this population). An average of 8 hours per patient was obtained from this sample with a corrected standard deviation of 1 hour.

Determine the upper limit of the 95% confidence interval for the average number of hours of sleep per patient in the population