the anal crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. Suppose you are a sociologist in Rock Springs, Wyoming, andom sample of police files showed that of 38 arrests last month, 21 were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. OH 0.7, p<0.7 OM₁ P=0.7; M₁1 P >0.7 Og P<0.7; H₂ P=0.7 OMg: P0.7; M₁ P=0.7 OH P-0.7; H₁: P0.7 (b) What sampling distribution will you use? O The standard normal, since np 5 and ng 5 O The Student's t, since np> 5 and ng S 5 O The Student's t, since np 5 and ng O The standard normal, since np 5 and no 5. What is the value of the sample test statistic (Round your answer to two decimal places) (c) Find the value of the test statistic. (Round your answer to four decimal places) W Sketch the sampling distribution and show the area corresponding to the P-value. -2 -1 0 1 2 0-3 -2 -2 0-3 0-3 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a O At the 0.01 level, we reject the null hypothesis and conclude the data are statistically significant O At the 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant Othea -0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a9.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. -1 0 A 0-3 -2 -10 3 -2 1 -1 0 (e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.01 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs effers from 70% an
the anal crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. Suppose you are a sociologist in Rock Springs, Wyoming, andom sample of police files showed that of 38 arrests last month, 21 were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. OH 0.7, p<0.7 OM₁ P=0.7; M₁1 P >0.7 Og P<0.7; H₂ P=0.7 OMg: P0.7; M₁ P=0.7 OH P-0.7; H₁: P0.7 (b) What sampling distribution will you use? O The standard normal, since np 5 and ng 5 O The Student's t, since np> 5 and ng S 5 O The Student's t, since np 5 and ng O The standard normal, since np 5 and no 5. What is the value of the sample test statistic (Round your answer to two decimal places) (c) Find the value of the test statistic. (Round your answer to four decimal places) W Sketch the sampling distribution and show the area corresponding to the P-value. -2 -1 0 1 2 0-3 -2 -2 0-3 0-3 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a O At the 0.01 level, we reject the null hypothesis and conclude the data are statistically significant O At the 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant Othea -0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a9.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. -1 0 A 0-3 -2 -10 3 -2 1 -1 0 (e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.01 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs effers from 70% an
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:**Title: Analyzing Crime Rate Demographics**
**Context:**
Is the national crime rate really going down? Some sociologists say yes! They propose that a reason for the decline in crime rates during the 1980s and 1990s is demographics. An aging population means fewer crimes are committed. Based on information from the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. As a sociologist in Rock Springs, Wyoming, you aim to understand these trends better.
**Objective:**
At the 1% level of significance, test the claim that the population proportion of such arrests in Rock Springs is different from 70%.
### Steps for the Analysis
**(a) Determine the Level of Significance:**
**State the Null and Alternate Hypotheses:**
- \( H_0: p = 0.7 \)
- \( H_1: p \neq 0.7 \)
**(b) Decide on the Sampling Distribution to Use:**
- Options:
- The standard normal, since \( np > 5 \) and \( n(1-p) > 5 \).
- The Student’s t, since \( n > 5 \) and \( n > 5 \).
**(c) Calculate the Value of the Sample Test Statistic:**
- Round your answer to two decimal places.
**(d) Find the P-value of the Test Statistic:**
- Round your answer to four decimal places.
**Sketch the Sampling Distribution and Show the Area Corresponding to the P-value.**
**Graphs of the Sampling Distributions:**
1. Four graphs are shown with normal distribution curves.
2. Each graph has a centered curve on a horizontal line marked from -3 to 3.
**(e) Based on Answers From (c) to (d), Decide Whether to Reject the Null Hypothesis at the 1% Significance Level:**
- \( \alpha = 0.01 \): Reject the null hypothesis if results are statistically significant.
### Conclusion:
1. **Reject or Fail to Reject the Null Hypothesis Based on Statistical Findings:**
- Determine whether the arrests in Rock Springs differ significantly from the national percentages.
2. **Interpret Your Conclusion:**
- Option 1: There is sufficient evidence at the 0.01 level to conclude the arrest proportion differs from 70%.
- Option 2
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