According to the U.S. Department of Justice, 27% of violent crimes in the U.S. i

Question

According to the U.S. Department of Justice, 27% of violent crimes in the U.S. involve the use of a weapon. A sample of crime information for last year in Cedarville indicated that 128 out of 400 crimes studied, or 32%, actually involved the use of a weapon. Assuming the claim of the U.S. Department of Justice is true, what is the probability that 27% or more of violent crimes in the U.S. involve the use of a weapon? a) 0.5000 b) 0.4346 c) 0.3012 d) 0.0821 What is the standard error of this sampling distribution? a) 0.0183 b) 0.0222 c) 0.0248 d) 0.0312 What is the probability of observing a sample proportion this large or larger? a) 0.0122 b) 0.0179 c) 0.0192 d) 0.0202

Explanation / Answer

19)

point estimate of proprotion of violent crimes i.e mean = 0.27

in normal distribution P(X<mean) = P(X>mean) = 0.5

so probability that 27% or more of violent crime in the USinvlove the use of a weapon

so answer is (a)

20)

sample size n = 400

point estimate of sample proportion i.e p = 0.27

standard error = [p*(1-p)/n]0.5 = [0.27*(1-0.27)/400]0.5 = 0.02219 ~0.0222 (b)

21)

z value for 0.32 is (0.32-0.27)/0.0222 = 2.2522, correspoding p value using z-table is 0.9878

P(X<0.32) = 0.9878

P(X>0.32)= 1-0.9878 = 0.0122 (a)

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