1. In a sample of 821 households in Morocco, the volume of water consumed in a week was 334 liters with a standard deviation of 591 liters. Test that the average volume of water consumed by Moroccan households in a week is different from 300 liters, using a 10% significance level.

2. A researcher wants to examine how the number of children affects mothers' labor force participation. In a sample of 141 mothers who had one child, the average number of weeks worked in 1979 was 20.65, with a standard deviation of 22.50. In a sample of 90 mothers who had 2 or more children, the average number of weeks worked in 1979 was 13.96, with a standard deviation of 20.70.

(a) Calculate a 90% confidence interval for the difference in the average number of hours worked in 1979 by mothers with one child versus mothers with 2 or more children. Assume different population standard deviations. Interpret the confidence interval.

(b) Test that mothers with one child work weekly at least 5 hours more on average than mothers with 2 or more children, using a 10% significance level.

3. 114 Canadian high-performance male athletes were surveyed, and their average caloric intake was 3077 kilocalo- ries per day, with a sample standard deviation of 987. The recommended minimum daily caloric intake is 3421.7 Using a 1% significance level, test whether Canadian high-performance male athletes are deficient in their caloric intake.