question archive A researcher wants to check the claim that convicted burglars spend less than 18
A researcher wants to check the claim that convicted burglars spend less than 18
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A researcher wants to check the claim that convicted burglars spend less than 18.7 months in jail, on average. She takes a random sample of 67 such cases from court files and finds that the mean is 16.8 months with a standard deviation of 7.3 months. Is there enough evidence to support the claim using a level of significance of 1%?
What is the decision based on the given sample statistics?
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H0: µ = 18.7
Ha: µ < 18.7
Test Statistic :-
t = ( X? - µ ) / (S / √(n) )
t = ( 16.8 - 18.7 ) / ( 7.3 / √(67) )
t = -2.13
From T table,
With test statistics of 2.13 and df of 66 ,
one tailed p-value = 0.0185
Since p-value > 0.01 level, fail to reject H0.
