An insurance company recorded the mean damage for a natural

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 can we concluded the prevention plans were effective in reducing the mean amount of claim?

Solution

4.

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   520  
Ha:    u   <   520   [ANSWER]

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b)
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    -   1.644853627   [ANSWER]

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c)  
              
Getting the test statistic, as              
              
X = sample mean =    501          
uo = hypothesized mean =    520          
n = sample size =    49          
s = standard deviation =    70          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.9          
              
As z < -1.6449, we   REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the prevention plans were effective in reducing the mean amount of claim. [CONCLUSION]