Question

Question 2. (30 Points): A random sampe 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 375 kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 81 kWh. (a) 10 points Assuming the standard deviation is unchanged and that the usage is normally distributed, determine the 99% confidence interval for the mean usage in the March quarter of 2006. (b) 5 points Denote X="Usage"~N(u, o). Given the hypothesis test HO: u = 330 versus H1: u # 330. What is your conclusion based on the analysis under (a) and why? (c) 10 points It is believed that only the standard deviation may have changed from the previous year. From the small data set given in 2006, the sample standard deviation is 91.5 kWh. Assuming that the usage is normally distributed, determine the 99% confidence interval for the mean usage in the March quarter of 2006. (d) 5 points Denote X="Usage"~N(u, o). Given the hypothesis test HO: u = 330 versus H1: # 330. What is your conclusion based on the analysis under (b) and why?

Answer 1

Answer usage is For given sample of size n=30, sample mean x = 375 kWh 0 ca) With o= 81 kWh, the gg. 1. confidence interval of mean wage in march quarter of 2006 is x + 2012 Jun for x=0,01 1 where Zx/2 = 2.576 2 s 375 2,576x81 30 = 375+ 38.09 : ( 336.90,413.09) N 3 we 4 2 (6) The hypotheses Hoill=330 VS HiiM7330 Since 'the mean wage value under Ho ie M = 330 and the gg.f confidence interval does not contain this null value, so conclude that mean usage in march quarte of 2006 is not equal to 330 kwh. Griven that 5 = 375, S= 91.5 kWh The gg.l. confidence interval for mean mage S when t(2,0-1) = 2.7564 for x=0.01, n=30 5 6 = tea, hall in 375 +2.7564x91,5, y 720 375 + 46.04 (320.96, 421,04)

(d) Given the hypotheses Ho: M=330 vs Hi : M # 230 Since the confidence interval obtained in (o contains the valu 14=330 under Ho, so we do not reject Ho at a = 0.01 level of significance and conclude that the mean usage in the march mean wage quarter of 2006 is 330kWh