Is the national 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. Accordi to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 yearst. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 36 arrests last month, 28 were of males aged 15 to years. Use a 10% 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. O Ho: P=0.7; H₁: p > 0.7 O Ho: P<0.7; H₁₂: P = 0.7 O Ho: P = 0.7; H₁: P = 0.7 O Ho: P = 0.7; H₁: P = 0.7 O Ho: P=0.7; H₂: P < 0.7 (b) What sampling distribution will you use? O The standard normal, since np > 5 and nq > 5. O The standard normal, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq> 5. O The Student's t, since np < 5 and ng < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) 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. 0-3 -2 -1 0 1 2 3 -1 0 1 2 3
Is the national 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. Accordi to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 yearst. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 36 arrests last month, 28 were of males aged 15 to years. Use a 10% 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. O Ho: P=0.7; H₁: p > 0.7 O Ho: P<0.7; H₁₂: P = 0.7 O Ho: P = 0.7; H₁: P = 0.7 O Ho: P = 0.7; H₁: P = 0.7 O Ho: P=0.7; H₂: P < 0.7 (b) What sampling distribution will you use? O The standard normal, since np > 5 and nq > 5. O The standard normal, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq> 5. O The Student's t, since np < 5 and ng < 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) 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. 0-3 -2 -1 0 1 2 3 -1 0 1 2 3
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Step 1: Determine the given variables.
VIEWStep 2: Idenify significance level and develop hypotheses for the test.
VIEWStep 3: Analyze the data using salt software.
VIEWStep 4: Identify the sampling distribution and find the test statistic.
VIEWStep 5: Find the P value and sketch the curve.
VIEWStep 6: Give the decision rule and interpret the conclusion.
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