An insurance company recorded the mean damage for a natural disaster in its area

Question

An insurance company recorded the mean damage for a natural disaster in its area was $520. After introducing several plans to prevent loss, it randomly samples 49 policyholders and finds the mean amount per claim was $501 with a standard deviation of $70. Use alpha = .05, can we concluded the prevention plans were effective in reducing the mean amount of claim? a. State the null and alternative hypotheses. H_0: H_1: b. What is the critical value of the test? c. What is the decision rule? d. Using the critical value approach, state your decision regarding H0.

Explanation / Answer

Ho:mean=520

Ha:mean<520

b) for 48 degree of freedom and at 0.05 level ; critical value =-1.6772

c)decision rule : reject Ho if test stat t<-1.6772

d)here std error=std deviation/(n)1/2 =10

hence test stat t=(X-mean)/std error =(501-520)/10=-1.9

as test stat is in critical region; reject Ho

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