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: Ho: 2010 - 2011 H1:/2010 < #2011 O Ho: P2010 P2011 H₁: P2010 > P2011 Ho: 2010/2011 H₁ 2010 2011 Ho: P2010 = P2011 H₁: P2010 P2011 O Ho: P2010 H₁: P2010 P2011 P2011 2011 O Ho: 2010 H₁: 2010> 2011 -3.33 b) Determine the test statistic. Round to two decimals. c) Find the p-value and round to 4 decimals.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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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:
Ho:μ2010 = μ2011
H1:/2010 < /2011
Ho: p2010
H1: P2010
Ho: 2010
H₁ 2010
p=
Ho: P2010
H₁: P2010
P2011
2 = -3.33
P2011
O Ho: P2010 = P2011
H1: P2010
P2011
2011
2011
d) Make a decision.
P2011
O Ho: 2010/2011
Ηι:μ2010 > μ2011
b) Determine the test statistic. Round to two decimals.
P2011
c) Find the p-value and round to 4 decimals.
Reject the null hypothesis
O Fail to reject the null hypothesis
e) Write the conclusion.
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.
Transcribed Image Text: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: Ho:μ2010 = μ2011 H1:/2010 < /2011 Ho: p2010 H1: P2010 Ho: 2010 H₁ 2010 p= Ho: P2010 H₁: P2010 P2011 2 = -3.33 P2011 O Ho: P2010 = P2011 H1: P2010 P2011 2011 2011 d) Make a decision. P2011 O Ho: 2010/2011 Ηι:μ2010 > μ2011 b) Determine the test statistic. Round to two decimals. P2011 c) Find the p-value and round to 4 decimals. Reject the null hypothesis O Fail to reject the null hypothesis e) Write the conclusion. 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.
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