Question

In: Statistics and Probability

Annual Returns Tech Firm Sample Finance Firm Sample 1 8.60% 1 10.10% 2 10.90% 2 8.80%...

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)

Solutions

Expert Solution

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

where

= 1.5363

degrees of freedom = n1+n2-2 = 24

tc = 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%

tc = 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


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