Question

Annual Returns		Tech Firm Sample			Finance Firm Sample
	1	8.60%		1	10.10%
	2	10.90%		2	8.80%
	3	13.10%		3	10.10%
	4	9.80%		4	12.20%
	5	11.40%		5	10.40%
	6	12.30%		6	7.30%
	7	10.90%		7	8.60%
	8	9.50%		8	12.10%
	9	13.10%		9	10.90%
	10	12.50%		10	9.50%
	11	12.70%		11	11.10%
	12	12.10%		12	10.80%
				13	10.40%
				14	12.50

Q8. Calculate the LCL and UCL for a 90% CI (α = 0.1) for the difference in mean returns between the two samples.

LCL ==>

UCL ==>

Based on this 90% interval, would you say the mean return for the Tech firms was higher than for Finance firms?(Yes/No)

Q9. Calculate the LCL and UCL for a 95% CI (α = 0.05) for the difference in mean returns between the two samples.

LCL ==>

UCL ==>

Based on this 95% interval, would you say the mean return for the Tech firms was higher than for Finance firms?(Yes/No)

Answer 1

8. 90% Confidence interval for difference in mean returns is

where

= 1.5363

degrees of freedom = n1+n2-2 = 24

t_c = 1.7109

thus 90% CI for difference in means is

= (11.4083-10.3429) 1.7109*1.5363*sqrt(1/12 +1/14)

= 1.0655    0.7025

= (0.363, 1.768)

LCL = 0.363

UCL = 1.768

Since 90% CI doesnot contain zero ,and both LCL and UCL have positive numbers , at 95% there is sufficient evidence to conclude that  the mean return for tech firm higher than finance firms.

For 95%

t_c = 2.0638

95% CI for difference in means

= (11.4083-10.3429) 2.0638*1.5363*sqrt(1/12 +1/14)

= 1.0655  0.8474

= (0.2181,1.9129)

LCL = 0.2181

UCL = 1.9189

Since 95% CI doesnot contain zero ,and both LCL and UCL have positive numbers ,at 95% there is sufficient evidence to conclude that  the mean return for tech firm higher than finance firms