Sampling Techniques and Statistical Inference Important Formulas

Dear students, before you start revision for the chapter Sampling Techniques and Statistical Inference, first make sure you revise all the formulas and key points. Only if you are thorough with the main concepts and formulas, you can confidently work out all the sums. That said, here are the most important formulas in Lesson 8 Sampling Techniques and Statistical Inference , Class 12 Business Maths.

Important Formulas Sampling Techniques and Statistical Inference

$\text{Sample}\\$
$\text{Sample size: n}\\$
$\text{Sample standard deviation: S}\\$
$\text{Sample variance:} S^{2}\\$
$\text{Sample Mean:} \;\bar{x}\\$
$\text{Sample proportion p} = \dfrac{x}{n};\; p+q=1\\$

$\text{Population}\\$
$\text{Population size: N}\\$
$\text{Population standard deviation: }\sigma\\$
$\text{Population variance:} \sigma ^{2}\\$
$\text{Population Mean:} \mu\\$
$\text{Population proportion= P;}\; p+q=1\\$

Confidence Interval for the Population Mean

$\bar{x}-z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}} \le \mu \le \bar{x}+z_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}}\\$

Normal Probability Table

Hypothesis testing

$\text{Null hypothesis} =(H_{0})\\$
$\text{Alternate hypothesis} =(H_{1})\\$
$\text{Test Statistic} \;z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\$

$If \left| z \right| > z_{\frac{\alpha}{2}}=1.96\; or\; 2.58\\$
$H_{0}\; \text{lies in the critical region. }H_{0} \;\text{is rejected.}\\$
$If \left| z \right| < z_{\frac{\alpha}{2}}=1.96\; or\; 2.58\\$
$H_{0}\; \text{lies in the acceptance region. }H_{0}\; \text{is accepted.} \\$

Solutions for Sampling Techniques and Statistical Inference Exercise 8.1

Solutions for Sampling Techniques and Statistical Inference Exercise 8.2

Solutions for Sampling Techniques and Statistical Inference Exercise 8.3

Statistic	Standard Error (S.E)
$\text{ Sample \;Mean}\; \bar{x} \\$	$\dfrac{\sigma}{\sqrt{n}} \\$
Observed Sample proportion p	$\sqrt{\dfrac{{pq}}{n}} \\$
Sample standard deviation s	$\sqrt{\dfrac{\sigma^{2}}{2n}}\\$
$\text{Sample variance} \;S^{2}\\$	$\sigma^{2}\sqrt{\dfrac{2}{n}}\\$
Sample quartiles	$1.36263\; \dfrac{\sigma}{\sqrt{n}}\\$
Sample median	$1.25331 \dfrac{\sigma}{\sqrt{n}}\\$
Sample correlation coefficient	$\dfrac{(1-p^{2})}{\sqrt{n}}\\$

$\text{Critical Values} \; z_{\alpha}\\$	1%	2%	5%	10%
Two tailed test	$\left\| z_{\alpha} \right\|=2.58\\$	$\left\| z_{\alpha} \right\|=2.33\\$	$\left\| z_{\alpha} \right\|=1.96\\$	$\left\| z_{\alpha} \right\|=1.645\\$
Right tailed test	$z_{\alpha} =2.33 \\$	$z_{\alpha} =2.055 \\$	$z_{\alpha} =1.645 \\$	$z_{\alpha} =1.28 \\$
Left tailed test	$z_{\alpha} =2.33 \\$	$z_{\alpha} =2.055 \\$	$z_{\alpha} =1.645 \\$	$z_{\alpha} =1.28 \\$

Sampling Techniques and Statistical Inference Important Formulas

Important Formulas Sampling Techniques and Statistical Inference

Confidence Interval for the Population Mean

Normal Probability Table

Hypothesis testing

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Important Formulas Sampling Techniques and Statistical Inference

Confidence Interval for the Population Mean

Normal Probability Table

Hypothesis testing

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