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

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Last Modified on September 8, 2013 by JoeStat

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