STATISTICS 8. : STATISTICS 1.ssdfasdfdas

Running head: STATISTICS 1
Statistics
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STATISTICS 2
Solution
Question 5
I. The 95% confidence interval for the true population man ROE.
Solution
The 95% confidence interval is determined in PhStat and is shown below:
confidence interval for the true populationmeanROE
Data
Sample StandardDeviation 12.80324744
Sample Mean 15.77
Sample Size 39
Confidence Level 95%
Standard Error of the Mean 2.050160376
Degrees of Freedom 38
t Value 2.0244
Interval Half Width 4.1503
Interval Lower Limit 11.6168
Interval Upper Limit 19.9175
Intermediate Calculations
Confidence Interval
From the above table, the confidence interval is 11.6168 ≤ μ ≤19.9175. It means that at
95% confidence interval, the true population mean for ROE is between 11.6168% and
19.9175%.
II. The 99% confidence interval for the true population mean DPS
Solution
The 99% confidence interval is determined in PhStat and is shown below:

STATISTICS 3
confidence interval for the true populationmeanDPS
Data
Sample StandardDeviation 1.803207723
Sample Mean 1.37
Sample Size 50
Confidence Level 99%
Standard Error of the Mean 0.255012082
Degrees of Freedom 49
t Value 2.6800
Interval Half Width 0.6834
Interval LowerLimit 0.6883
Interval Upper Limit 2.0552
Intermediate Calculations
Confidence Interval
From the above table, the confidence interval is 0.6883 ≤ μ ≤ 2.0552. It means that at 99%
confidence interval, the true population mean for DPS is between 0.6883 and 2.0552.
III. The 90% confidence interval for the true proportion of all companies whose
dividend yield is better than 10%
Solution
The table below summarizes the confidence interval of the proportion.
Data
Sample Size 50
Number of Successes 14
Confidence Level 90%
Sample Proportion 0.28
ZValue -1.6449
Standard Error of the Proportion 0.0635
Interval Half Width 0.1044
Interval Lower Limit 0.1756
Interval Upper Limit 0.3844
Intermediate Calculations
Confidence Interval
From the above table, the confidence interval is 0. 1756 ≤ p ≤ 0.3844. It means that at 90%
confidence interval, the true population proportion of all companies whose dividend yield
is better than 10% is between 0.1756 and 0.3844.