In: Statistics and Probability
The following information was obtained from independent random samples. The Degrees of Freedom have be calculated to be 19. The Standard Deviations are Unknown. | ||||||
Small Sample Size: Use t-value | ||||||
Sample 1 | Sample 2 | |||||
Sample Mean | 45 | 42 | ||||
Sample Variance | 85 | 90 | ||||
Sample Standard Deviation | ||||||
Sample Size | 10 | 12 | ||||
Standard Error | ||||||
Confidence Coefficient | 0.95 | |||||
Level of Significance | ||||||
Degrees of Freedom | 19 | |||||
t-value | ||||||
Margin of Error | ||||||
Point Estimate of Difference | 3 | |||||
Lower Limit | ||||||
Upper Limit |
The 95% confidence interval for the difference between the two population means is | ||||||
to |
Degree of freedom, DF=
19
t-critical value = t α/2 =
2.093 (excel formula
=t.inv(α/2,df)
std error , SE = √(s1²/n1+s2²/n2) =
4.000
margin of error, E = t*SE = 2.093
* 4.000 = 8.3721
difference of means = x̅1-x̅2 = 45.0000
- 42.000 = 3.0000
confidence interval is
Interval Lower Limit = (x̅1-x̅2) - E =
3.0000 - 8.372 =
-5.3721
Interval Upper Limit = (x̅1-x̅2) + E =
3.0000 - 8.372 =
11.3721
CI (-5.3721 , 11.3721)
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