8 The average number of violent crimes per 100000 inhabitant

8. The average number of violent crimes per 100,000 inhabitants in the U.S. in 2006 was 431.52. Assume we know the population standard deviation for the number of? violent crimes per 100,000 inhabitants is 238.38. Suppose we want to sec if there has been a significant decrease in the number of violent crimes. We take a sample of 30 states in 2013 and find that the average number of violent crimes per 100,000 inhabitants is 365.46. Use (alpha =.10. a. What are the null and alternative hypotheses? b. What is the critical value? c. Calculate the test statistic. d. Find the p-value. e. What conclusion is made here?

Solution

Mean = 431.52
Population SD = 238.38
n=30
X = 365.46
alpha =0.10
dF=30-1 = 29

a)
Null Hypothesis :
H0: mu < 431.52
Alternate Hypothesis :
H1 : mu >= 431.25

b)
Critical value = 1.31 Answer

c)
Test static t = (X -mu)/(SD/sqrt(n))
= (365.46 - 431.25)/(238.38/sqrt(30))
= -1.52 Answer

d)
P-value = 0.07 Answer

e)
Since P-value < 0.1 , Reject null hypothesis.