Confidence Interval Formula for Two Populations

If The Two Populations Are Dependent

Confidence Interval Dependant is \widehat{p}_1-\widehat{p}_2)-E<(p_1-p_2)<(\widehat{p}_1-\widehat{p}_2)-E

Confince Interval Dependent formula is E=z _{\alpha /2} \sqrt{ \frac{ \widehat{p} _1 \widehat{q} _1} {n_1}+ \frac{ \widehat{p} _2 \widehat{q} _2} {n_2}}

If The Two Populations Are Independent

If Two Populations are independent \widehat{x}_1-\widehat{x}_2)-E<(\mu_1-\mu_2)<(\widehat{x}_1-\widehat{x}_2)-E

(assuming Sigma 1 Symbol  and sigma 2 symbol are unknown and assumed to not be equal)
Confidence Interval sigmas known and not equal E=t _{\alpha /2} \sqrt{ \frac{ s_1 ^2}{n_1}+\frac{s_2 ^2}{n_2}}

Degrees of Freedom for Confidence Interval E=t _{\alpha /2} \sqrt{ \frac{ s_1 ^2}{n_1}+\frac{s_2 ^2}{n_2}}

(assuming Sigma 1 Symbol and sigma 2 symbol are unknown and assumed to be equal)

Confidence Interval E=t _\alpha /2 \sqrt{ \frac{ s_p ^2} {n_1}+ \frac{ s_p ^2}{n_2}

DF E=t _\alpha /2 \sqrt{ \frac{ s_p ^2} {n_1}+ \frac{ s_p ^2}{n_2}

s_p ^2 = \frac{(n_1 - 1)s_1 ^2+(n_2-1)s_2 ^2}{(n_1-1)+(n_2-1)}

 

(Sigma 1 Symbol and sigma 2 symbol are known)

CI E=z _\alpha /2 \sqrt{ \frac{ \sigma _1 ^2}{n_1}+\frac{\sigma _2 ^2}{n_2}}

For Matched Pairs

\bar{d} -E < \mu _d < \bar{d} + E

 E=z _ {\alpha /2} \cdot [\frac{s_d}{\sqrt{n}}]

 df = n - 1




Last Modified on September 8, 2013 by JoeStat

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