SOLUTION: Test the claim that the mean age of the prison population in cone city is less than 26 years. Sample data are summarized as n=25, mean= 24.4, s=9.2 and a=.05
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-> SOLUTION: Test the claim that the mean age of the prison population in cone city is less than 26 years. Sample data are summarized as n=25, mean= 24.4, s=9.2 and a=.05
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Question 875125: Test the claim that the mean age of the prison population in cone city is less than 26 years. Sample data are summarized as n=25, mean= 24.4, s=9.2 and a=.05
This is not for home just for study...thank you! Answer by jim_thompson5910(35256) (Show Source):
We are using the T distribution because
a) we do not know the population standard deviation (very common in most cases)
b) n < 30
t = (xbar - mu)/(s/sqrt(n))
t = (24.4 - 26)/(9.2/sqrt(25))
t = -0.8695652173913
t = -0.87
This is a one tailed test to the left, so we want to find the area to the left of t = -0.87.
Due to symmetry, this is the same as finding the area to the right of t = 0.87
Use a table like this one to find the area to the right of 0.87 to be between 0.15 and 0.20
How am I getting this? The sample size is n = 25, so the there are 25 - 1 = 24 degrees of freedom, df = 24.
We look in the df = 24 row and we are looking for 0.87, but unfortunately it's not in the row; however, we know it's between 0.857 and 1.059.
The probabilities for the one tailed test are 0.20 and 0.15 respectively, so that's how I got the area to be between 0.15 and 0.20
Anyways, the area to the right of t = 0.87 is between 0.15 and 0.20
So the area to the left of t = -0.87 is between 0.15 and 0.20
The p-value is NOT less than 0.05 (the given significance level alpha). Even if the p-value was the smallest it can get (0.15), it is still not even close to being smaller than 0.05.
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