Question

A concerned group of citizens wanted to know if the proportion of armed robberies in Texas was different in 2011 than in 2010. Their research showed that of the 113,231 violent crimes in Texas in 2010, 7,622 of them were armed robberies. In 2011, 7,439 of the 104,873 violent crimes were in the armed robbery category. Test at a 5% significance level.

a) The null and alternative hypothesis would be: Select one.

H0:p2010=p2011H0:p2010=p2011
H1:p2010≠p2011H1:p2010≠p2011

H0:μ2010=μ2011H0:μ2010=μ2011
H1:μ2010<μ2011H1:μ2010<μ2011

H0:μ2010=μ2011H0:μ2010=μ2011
H1:μ2010≠μ2011H1:μ2010≠μ2011

H0:μ2010=μ2011H0:μ2010=μ2011
H1:μ2010>μ2011H1:μ2010>μ2011

H0:p2010=p2011H0:p2010=p2011
H1:p2010>p2011H1:p2010>p2011

H0:p2010=p2011H0:p2010=p2011
H1:p2010<p2011H1:p2010<p2011

b) Determine the test statistic. Round to two decimals.

z=_____

c) Find the p-value and round to 4 decimals.

p = ____

d) Make a decision. Select one.

-Fail to reject the null hypothesis

-Reject the null hypothesis

e) Write the conclusion. Select one.

-There is sufficient evidence to support the claim that the proportion of armed robberies is different in 2011 than 2010.

-There is not sufficient evidence to support the claim that the proportion of armed robberies is different in 2011 than 2010.

Answer 1

Answer:

a)

Given,

Ho : =

Ha : !=

sample proportion p1 = x1/n1 = 0.067

p2 = x2/n2 = 0.071

p^ = (x1 + x2)/(n1 + n2)

on solving we get

p^ = 0.069

q^ = 1 - p^ = 1 - 0.069 = 0.931

b)

Consider,

test statistic z = (p1 - p2)/sqrt(p^*q^(1/n1 + 1/n2))

substitute values

= (0.067 - 0.071)/sqrt(0.069*0.931(1/113231 + 1/104873))

= - 3.68

c)

P value = 0.0002332 [since from z table]

= 0.0002

d)

Here we observe that, p value < alpha, so we reject Ho.

e)

So there is a sufficient evidence to support the claim.