In: Statistics and Probability
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) |
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