Further Stats Chapter 4: Hypothesis Testing

9 flashcards · Mathematics · by TheoTyson

  1. What are the two hypothesises for a Poisson distribution hypothesis test?

    The null hypothesis H0:λ=mH_0 : \lambda = mH0​:λ=m . Single tail alternative hypothesis H1:λ<mH_1 : \lambda < m H1​:λ<m or m"> λ>m\lambda > mλ>m . Two tail alternative hypothesis H1:λ≠mH_1 : \lambda \neq mH1​:λ=m .

  2. How do you find the ppp -value for a Poisson or geometric distribution hypothesis test?

    Assume the null hypothesis is true, and the number given in the question is x.

  3. Which value of the cumulative Poisson distribution do you calculate if H1:λ<mH_1 : \lambda < m H1​:λ<m or m"> H1:λ>mH_1 : \lambda > mH1​:λ>m ?

    If H1:λ<mH_1 : \lambda < mH1​:λ<m calculate P(X⩽x)P(X \leqslant x)P(X⩽x) . If m"> H1:λ>mH_1 : \lambda > mH1​:λ>m calculate P(X⩾x)P(X \geqslant x)P(X⩾x) .

  4. Do you accept or reject H0H_0H0​ if P<αP < \alphaP<α ?

    There is sufficient evidence to reject H0H_0H0​ .

  5. Do you accept or reject H0H_0H0​ if \alpha"> P>αP > \alphaP>α ?

    There is insufficient evident to reject H0H_0H0​ , accept H0H_0H0​ .

  6. How do you find the critical values for a Poisson or geometric distribution hypothesis test?

    Find the value of x that gives a P(X⩽x)<αP(X\leqslant x) < \alphaP(X⩽x)<α or the value of x that gives a \alpha"> P(X⩾x)>αP(X\geqslant x) > \alphaP(X⩾x)>α .

  7. What is different for a two tailed test?

    The significance needs to be halved, the critical region will have two halves.

  8. What are the two hypothesises for a geometric distribution hypothesis test?

    The null hypothesis H0:p=mH_0 : p = mH0​:p=m . Single tail alternative hypothesis H1:p<mH_1 : p < mH1​:p<m or m"> p>mp > mp>m . Two tail alternative hypothesis H1:p≠mH_1 : p \neq mH1​:p=m .

  9. Which value of the cumulative geometric distribution do you calculate if H1:p<mH_1 : p < mH1​:p<m or m"> H1:p>mH_1 : p > mH1​:p>m ?

    If H1:p<mH_1 : p < mH1​:p<m calculate P(X⩽x)P(X \leqslant x)P(X⩽x) . If m"> H1:p>mH_1 : p > mH1​:p>m calculate P(X⩾x)P(X \geqslant x)P(X⩾x) .