There are two main brands of ultrasonic humidifiers. suppose a simple random sample of 125 humidifiers is selected from each brand. for each sampled humidifier, the output of moisture (in oz) was measured in a controlled chamber. the average measurement for the humidifiers of the first (resp. second) brand was 12.7 (resp. 12) and the corresponding standard deviation was 2.5 (resp. 2). (a) obtain an approximate 95% confidence interval for the difference between the average output among all humidifiers of the first brand and the average output among all humidifiers of the second brand. does it include 0? (b) test the hypothesis that there is no difference between the average outputs of the two brands at a 5% significance level.