It is believed that the percent of convicted felons who have a history of juvenile delinquency is 70%. Is there evidence to support the claim that the actual percentage is more than 70% if out of 200 convicted felons, we find that 154 have a history of juvenile delinquency? Set the level of significance at ?=0.05. d) Sketch the z curve indicating the z test statistic and the p-value. e) Should you reject or fail to reject the null hypothesis based on the p-value obtained in the previous part? Why? f) State your conclusion from the test.
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Step 1: The null hypothesis is that the percentage of convicted felons with a history of juvenile delinquency is 70%, while the alternative hypothesis is that the percentage is greater than 70%. Show more…
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A delinquency offense is an act committed by a juvenile for which an adult could be prosecuted in a criminal court. The following data represent the number of various types of delinquencies by gender in a random sample of 750 delinquencies. (a) Does the evidence suggest that gender is independent of type of delinquency at the $\alpha=0.05$ level of significance? (b) Compute the $P$ -value for this test by finding the area under the chi-square distribution to the right of the test statistic. (c) Construct a conditional distribution by type of delinquency and draw a bar graph. Does this evidence support your conclusion in part (a)?
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Suppose we are contracted by the Justice Department to study the extent of juvenile delinquency. We take a random sample of 100 juveniles, and we find that the mean number of crimes committed is 12 with a standard deviation of 7. 1. Construct a 95% confidence interval for the mean number of crimes committed by the population of juveniles. 2. Interpret the meaning of this interval. 3. Test the null hypothesis that the mean number of crimes committed by the population of juveniles is less than or equal to 11. Use a significance level of .05. 4. If you rejected the null hypothesis, explain why. If you failed to reject the null hypothesis, explain why. (Be sure to use the concept of probability in your answer).
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