A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2006. The average usage was found to be 375kWh.
In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed, provide an expression for calculating a 98% confidence interval for the mean usage in the March quarter of 2006.
It is believed that the standard deviation from the population has changed and thus is unknown. However, from the small data set in 2006, we know the sample standard deviation is 91.5kWh. Assuming that the usage is normally distributed, provide an expression for calculating a 98% confidence interval for the mean usage in the March quarter of 2006.