Question

According to the U.S. FBI Statistics, during 2015 there was an average rate of 3.86 violent crimes per 1,000 residents in the U.S. population. Data was collected from a sample of Arizona cities (www.ucr.fbi.gov) to determine whether the violent crime rate in Arizona differs from the national rate of violent crime. The data results are shown below: Use α = .05 Rate of Violent Crime per 1000 Residents in Arizona Cities Chandler = 1.89 Mesa = 4.19 Tempe 4.11 Scottsdale =1.86 Gilbert = 0.72 Apache Junc.= 2.49 Peoria = 1.66 Phoenix = 5.94 Maricopa = 1.72 Glendale = 3.92 Avondale = 3.46 Surprise = 1.31 Please state what type of t -test should be used, then show all 4 steps of the hypothesis test and include cohen's d and the confidence interval. upload your calculations. Please write the number of the problem, the type of t test, then all four steps. Use proper notation. Please write clearly and in an organized way by squaring or circling the answers in the calculations in step 3.

Answer 1

a)
Ho: μ = 3.86
Ha: μ ≠ 3.86

Independent measures t-test

b)

If |t|> t(table value) then H0 is to be rejected.

Critical value for a two-tailed test is t = 2.201

c)

Sample mean = 33.27/12 = 2.77

n=12

sd= √{(1.89 - 2.7725)2 + ... + (1.31 - 2.7725)^2/(12 - 1)}
=√2.3644568181818
= 1.54

Therefore, t = (2.77-3.86)/(1.54/√12)

= -2.452

d)

Since |t|=2.452>2.201, H0 is rejected.

Therefore, there is enough evidence to claim that the population mean μ is different than 3.86, at the 0.05 significance level.

Cohen's d = 2t /√(df) = 4.904/3.3166 = -1.4786 = -1.48

95% Confidence Interval: 2.77 ± 0.871 = (1.9, 3.64)

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