The maintenance crew of a hotel has to monitor the temperature of the hotel pool and hot tub. To enhance comfort, the management
team requests that the mean pool temperature and the mean hot tub temperatures not differ by more than 15 degrees. To estimate the difference in these mean temperatures the maintenance crew selects a random sample of 8 times to check the hot tub temperature and a random sample of 10 times to check the pool temperature. Although the sample sizes are small, the distribution of temperature for the pool and for the hot tub does not show strong skewness or any outliers. The mean pool temperature is 86 degrees with a standard deviation of 3 degrees. The mean hot tub temperature is 101 with a standard deviation of 1.8 degrees. What is the correct 95% confidence interval for the true difference in the population means (hot tub – pool)? Use the conservative df.
