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A chi square test is conducted to check whether a person's ability in Mathematics has an impact on his/her interest in Statistic. The test statistic is 13.277 under the tested null hypothesis. write a recommended null hypothesis and an alternative hypothesis. Briefly describe your conclusion on this test at the 0.01 significance level.

ChampR
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1 Answers1

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Alternative hypothesis (what the study is trying to find out): interest in statistics is not the same on average for people of all mathematical abilities Null hypothesis (negation of the alternative hypothesis): interest in statistics is the same on average for people of all mathematical abilities

If there are at least four degrees of freedom, then the test is significant at the 0.001 level. The p-value can be found in R using the command pchisq(13.277,k) where k is the number of degrees of freedom. Alternatively, the p-value is given by

$1-\frac{1}{\Gamma(\frac{k}{2})}\gamma(\frac{k}{2},\frac{x}{2})$

where $\gamma(s,x)=\int_0^xt^{s-1}e^{-t}dt$

Angela Pretorius
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  • It is unclear from the problem statement how many degrees of freedom are present, so it is reasonable to frame an answer that conditions how significant the $\chi^2$ outcome is on an assumption about degrees of freedom. At first reading the Question suggested to me that a $2\times 2$ contingency table would be the outcome, which would only have one degree of freedom. – hardmath Dec 18 '15 at 09:33