Guidelines for Hypothesis Testing

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<ul><li><p>8/2/2019 Guidelines for Hypothesis Testing</p><p> 1/6</p><p>Hypothesis Testing</p><p>HypothesisTesting Null Hypothesis Test statistic</p><p>Testing hypothesis about</p><p>population means Ho: = or &gt; or &lt; specified value</p><p>i. s is known &amp; population is normal Normal: zii. s is known &amp; sample size is 30 Normal: z</p><p>Ho: = or &gt; or &lt; specified value</p><p>population is normal but s is not known t statistic: t</p><p>Testing hypothesis about</p><p>population proportions Ho: p= or &gt; or &lt; specified valuei. If binomial probabilities can be calculated</p><p>i.e. n, the no. of trials &amp; p probability of</p><p>success should be given; sample size should</p><p>be 500 binomial</p><p>ii. If n &gt; 500, then normal approximation is</p><p>used Normal: z</p><p>Testing hypothesis about</p><p>population variance Ho: s2= or &gt; or &lt; specified value Chi square: c2</p><p>Testing hypothesis with</p><p>respect to comaprison of</p><p>paired observations Ho: 1 - 2 0 Paired t</p><p>Testing hypothesis for</p><p>differences between</p><p>population means Ho: 1 - 2 a particular value</p><p>i. when sample sizes n1 &amp; n2 are both</p><p>atleast 30 &amp; population std. deviations s1 &amp;s2 are known ii.Both populations are normally distributed &amp;</p><p>the population std. deviations s1 &amp; s2 areknown Normal: z</p></li><li><p>8/2/2019 Guidelines for Hypothesis Testing</p><p> 2/6</p><p>iii. Both populations are normally</p><p>distributed, population std. deviations are</p><p>unknown but both sample standard</p><p>deviations are known t statistic</p><p>Testing hypothesis for</p><p>differences between two</p><p>population proportions for</p><p>large samples</p><p>Ho: p1 - p2 zero or a particular</p><p>value Normal: z</p><p>Testing hypothesis for</p><p>equality of two population</p><p>variances Ho: s12 = s22 F distribution</p><p>ANOVA Ho: 1 = 2 = 3</p><p>Note: Pls refer Complete Business Statistics by Amir Aczel &amp; J. Sounderpandian pg - 295- 352</p></li><li><p>8/2/2019 Guidelines for Hypothesis Testing</p><p> 3/6</p><p>Formula</p><p>(x bar - m)/ sn(x bar - m)/ sn</p><p>(x bar - m)/ sn</p><p>P (X = x) =ncx .p</p><p>x.q</p><p>n-x</p><p>p -p0/p0 (1-p0)/n}</p><p>(n-1)S2/s0</p><p>2</p><p>t = {(x1 bar - x2 bar) - (1 - 2)o}/sp(1/n1+1/n2)</p><p>where sp is the combined standard deviation of the two samples given</p><p>as sp = [(n1-1) s12</p><p>- (n2-1)s22/(n1-1)+(n2-1)]</p><p>z = {(x1 bar - x2 bar) - (m1 m2)(s12n1)+ (s22n2)</p></li><li><p>8/2/2019 Guidelines for Hypothesis Testing</p><p> 4/6</p><p>t = {(x1 bar - x2 bar) - (m1 m2)sp2(1n1+ 1n2)</p><p>z = {(p1 - p2) - (p1 - p2)o}/p(1-p)(1/n1+1/n2)} where p =(x1 + x2)/(n1 + n2)</p><p>F = (c12/k1)/(c22/k2)where c12is a chi-square random variable with k1 df</p><p>&amp; c22 is another independent chi-square variable with k2 df</p><p>for further reference</p></li><li><p>8/2/2019 Guidelines for Hypothesis Testing</p><p> 5/6</p><p>Non - parametric test: these are used mainly</p><p>when population distributrions are not</p><p>normal</p><p>Sign test</p><p>Mann Whitney U test</p></li><li><p>8/2/2019 Guidelines for Hypothesis Testing</p><p> 6/6</p><p>Kruskal-Wallis</p></li></ul>