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 p-value for this hypothesis test? Round your answer to four decimal places.
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Here, the null and alternative hypothesis are;
H0 : µ = 18.7
Ha : µ < 18.7
Given;
n = 67
Standard deviation sd = 7.3
x bar = 16.8
We know that Z is given by the formula;
Z = (x bar-µ)/(sd/√n)
= (16.8-18.7)/(7.3/√67)
= -2.130
From the standard normal distribution table;
P(Z<-2.130) = 0.01659
Therefore, p value = 0.0166
Given that the level of significance α = 1% = 0.01 which is less than the calculated p value (p value > 0.01), this research does not reject the null hypothesis meaning that there is no enough evidence to support the claim.
