**Title: Statistical Analysis of Armed Robbery Rates in Texas for 2010 and 2011**A concerned group of citizens sought to determine whether the proportion of armed robberies in Texas differed in 2011 compared to 2010. Research reveals that out of 113,231 violent crimes in Texas in 2010, 7,622 were armed robberies. In 2011, there were 7,439 armed robberies out of 104,873 violent crimes. This study is conducted at a 0.05 significance level.**Preliminary Steps:**1. **Assumption Check:** - Is it safe to assume that: - The 2010 armed robberies comprise less than or equal to 5% of all violent crimes? - The 2011 armed robberies comprise less than or equal to 5% of all violent crimes? - Options: No ( ) Yes ( )2. **Sample Size Verification:** - Verify that \(np(1 - \hat{p}) \geq 10\). Round your answers to one decimal place. - \(n_{2010}\hat{p}(1 - \hat{p}) = \_\_\_\_\_\_\_\) - \(n_{2011}\hat{p}(1 - \hat{p}) = \_\_\_\_\_\_\_\)**Testing the Claim:**1. **Formulate Hypotheses:** - Null Hypothesis (\(H_0\)): \(p_{2010} = p_{2011}\) - Alternative Hypothesis (\(H_a\)): \(p_{2010} \neq p_{2011}\)2. **Calculate Test Statistic:** - Determine the value of \(z\) and round it to two decimal places. - \(z = \_\_\_\_\_\_\_\)3. **Determine p-value:** - Calculate the p-value and round it to four decimal places. - \(p\text{-value} = \_\_\_\_\_\_\_\)4. **Make a Decision:** - Options: - Fail to reject the null hypothesis. - Reject the null hypothesis.5. **Conclusion:** - If evidence supports the claim, conclude: - There is sufficient evidence to suggest that the proportion of armed robberies was different in 2011 compared to

Given, x1 = 7622 x2 = 7439 p̂1=x1/n1 = 0.0673 p̂2=x2/n2 = 0.0709 n1 = 113231 n2 = 104873a)Yes b) n2010p^(1-p^)= 7108.9 n2011p^(1-p^)= 6911.3 a) Null Hypothesis: H0: p1=p2 Alternate Hypothesis: Ha: p1≠p2 b) p^=x/n= 0.0673 0.0709 estimated prop. diff =p̂1-p̂2 = -0.0036 pooled prop p̂ =(x1+x2)/(n1+n2)= 0.0691 std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) = 0.0011 test stat z=(p̂1-p̂2)/Se = -3.33 c) p value =0.000869 d) As p value is less than significance level, Reject the null hypothesis e) There is sufficient evidence to support the claim that the proportion of armed robberies is different in 2011 than 2010

Math

Statistics

A concerned group of citizens wanted to determine whether the proportion of armed robberies in the state of Texas was different in 2011 than in 2010. Research shows 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 robery category. Test at the 0.05 significance level. Preliminary: a. Is it safe to assume that n2010 < 5 % of all violent crimes during 2010 and n2011 < 5% of all violent crimes during 2011? No Yes b. Verify np(1 - p) > 10. Round your answer to one cimal place. n2010P (1 – p) = n2011P (1 – p) = %3| Test the claim: a. Determine the null and alternative hypotheses. Ho: P2010 ? Ha: P2010 ? P2011 P2011 b. Determine the test statistic. Round to two decimal places. c. Find the p-value. Round to four decimals. p-value = d. Make a decision. Fail to reject the null hypothesis. 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.

A concerned group of citizens wanted to determine whether the proportion of armed robberies in the state of Texas was different in 2011 than in 2010. Research shows 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 robery category. Test at the 0.05 significance level. Preliminary: a. Is it safe to assume that n2010 < 5 % of all violent crimes during 2010 and n2011 < 5% of all violent crimes during 2011? No Yes b. Verify np(1 - p) > 10. Round your answer to one cimal place. n2010P (1 – p) = n2011P (1 – p) = %3| Test the claim: a. Determine the null and alternative hypotheses. Ho: P2010 ? Ha: P2010 ? P2011 P2011 b. Determine the test statistic. Round to two decimal places. c. Find the p-value. Round to four decimals. p-value = d. Make a decision. Fail to reject the null hypothesis. 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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