A local politician, running for reelection, claims that the mean prison time for
ID: 3362654 • Letter: A
Question
A local politician, running for reelection, claims that the mean prison time for car thieves is less than the required 4 years. A sample of 25 convicted car thieves was randomly selected, and the mean length of prison time was found to be 3 years and 6 months, with a standard deviation of 1 year and 3 months. At = 0.05, test the politician's claim. 4. A study was conducted to determine if the salaries of elementary school teachers from two neighboring states were equal. A sample of 100 teachers from each state was randomly selected. The mean from the first state was $28,700 with a standard deviation of $2300. The mean from the second state was $30,100 with a standard deviation of $2100. Test the claim that the salaries from both states are equal. Use = 0.10. 5.Explanation / Answer
Given that,
population mean(u)= 4 years = 48 months
standard deviation, = 1 yr 3 months = 15 months
sample mean, x = 3 year 6 months = 42 months
number (n)=25
null, Ho: =48
alternate, H1: <48
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 42-48/(15/sqrt(25)
zo = -2
| zo | = 2
critical value
the value of |z | at los 5% is 1.645
we got |zo| =2 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : left tail - ha : ( p < -2 ) = 0.02
hence value of p0.05 > 0.02, here we reject Ho
ANSWERS
---------------
null, Ho: =48
alternate, H1: <48
test statistic: -2
critical value: -1.645
decision: reject Ho
p-value: 0.02
we have evidence that mean prison time for car theives is less than 4 years
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