Question

A town that recently started a single-stream recycling program provided 60-gallon recycling bins to 25 randomly selected households and 75-gallon recycling bins to 21randomly selected households. The average total volumes of recycling over a 10-week period were 385 and 412 gallons for the two groups, respectively, with standard deviations of 59.7 and 32.6 gallons, respectively. Suppose that thestandard deviations for the two populations are not equal. Constructa 98% confidence intervalfor the difference in the mean volumes of 10 -week recycling for the households with the 60-gallon and 75-gallon bins.Let μ1 be the mean volume of 10-week recycling for the households with the 60-gallon bins and μ2 be the mean volume of 10-week recycling for the households with the 75-gallon bins. Round your answers to two decimal places. Enter your answer; confidence interval, lower bound

Answer 1

The 98% confidence interval for the difference between the population means with unequal variances is given as

Here the degrees of freedom is given as

From the given samples,

Now substitute these values in the formula for the degrees of freedom.

Now substitute the sample means, sample standard deviations and degrees of freedom in the confidence interval.

The 98% confidence interval for the mean difference in volumes between the group 1 households and group 2 households is (-60.76, 6.76)

The lower bound is -60.76 and the upper bound is 6.76.