Formular Number 
Name 
Formular 
Formular with R


6.2.1 
Expression of an interval estimate 
estimator ± (reliability coefficient)× standard error of the estimator

Example

6.2.2 
Interval estimate for $\mu$ when $\sigma$ is known 
${\bar {X}}\pm z_{(1\alpha /2)}\sigma _{\bar {x}}$

Example

6.3.1 
ttransformation 
$t={\frac {{\bar {x}}\mu }{s/{\sqrt {n}}}}$ 
Example

6.3.2 
Interval estimate for $\mu$ when $\sigma$ is unknown 
${\bar {X}}\pm t_{(1\alpha /2)}{\frac {s}{\sqrt {n}}}$ 
Example

6.4.1 
Interval estimate for the difference between two population means when $\sigma _{1}$ and $\sigma _{2}$ are known 
$({\bar {x}}_{1}{\bar {x}}_{2})\pm z_{(1\alpha /2)}{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}$ 
Example

6.4.2 
Pooled variance estimate 
$s_{p}^{2}={\frac {(n_{1}1)s_{1}^{2}+(n_{2}1)s_{2}^{2}}{n_{1}+n_{2}2}}$ 
Example

6.4.3 
Standard error of estimate 
$s_{({\bar {X}}_{1}{\bar {X}}_{2})}={\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}$ 
Example

6.4.4 
Interval estimate for the difference between two population means when s 1 is unknown 
$({\bar {x}}_{1}{\bar {x}}_{2})\pm t_{(1\alpha /2)}{\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}$ 
Example

6.4.5 
Cochran’s correction for reliability coefficient when variances are not equal 
$t'_{(1\alpha /2)}={\frac {w_{1}t_{1}+w_{2}t_{2}}{w_{1}+w_{2}}}$ 
Example

6.4.6 
Interval estimate using Cochran’s correction for t 
$({\bar {x}}_{1}{\bar {x}}_{2})\pm t'_{(1\alpha /2)}{\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}$ 
Example

6.5.1 
Interval estimate for a population proportion 

Example

6.6.1 
Interval estimate for the difference between two population proportions 

Example

6.7.1–6.7.3 
Sample size determination when sampling with replacement 

Example

6.7.4–6.7.5 
Sample size determination when sampling without replacement 

Example

6.8.1 
Sample size determination for proportions when sampling with replacement 

Example

6.8.2 
Sample size determination for proportions when sampling without replacement 

Example

6.9.1 
Interval estimate for s 2 

Example

6.9.2 
Interval estimate for s 

Example

6.10.1 
Interval estimate for the ratio of two variances 

Example

6.10.2 
Relationship among F ratios 

Example

Symbol Key 
