Question

QUESTION 4 A survey of 100 businesses revealed that the mean after-tax profit was $80,000 and the standard deviation was $12,000. Determine the 90% confidence interval estimate of the mean after-tax profit. (77540, 82460] b. [76130, 83870) C-[77060, 82940) d. 76904, 83096] [78032, 81968] QUESTION 5 A random sample of 400 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) used last quarter was recorded for each household in the sample. The average usage was found to be 377.55 kWh. The standard deviation of the usage was 25 kWh. Find the upper confidence limit of the 95% confidence interval for the mean usage in the last quarter. a 388 kWh b. 386 kWh C. 380 kWh d. 384 kWh e. 382 kWh

Answer 1

Date: Solution Given that, X 80.000 0= 12,000 n = 100 At 90% Confidence level z is, 2-1-90% = 1-0.90 -0.10 X/2=0.05 Z212= 20.05 = 1.64 E = Zx12x E=1.64X 12,000 a Joo E = 1968 A 90 % Confidence interval is, X- E <uk ž + E 80,000 -1968 <ul 80,000 + 1968 78032 Lul 81968 (78032, 81968) option 'e' is correct

Page No.: Date: Solution Given that X = 377.55 6 = 25 n = 4oo At 95% Confidence level the 2 is, 2 =1-95 % = 1-0.95 -0.05 2/2 20.025 za12 - Z0.025 - 1.96 E- Z412 x 25 E - 1.96 X 5400 E = 2.45 A 95% Confidence interval is, X + E 377.55+ 2.45 (380) Option C is correct