B. 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).

C. Suppose we wish to make an estimate of the proportion of the population that has a learning disability.We take a random sample of 100 people.In this sample, 15% of the respondents have a learning disability.

1. Construct a 95% confidence interval for the proportion of people in the population who have a learning disability.

2. Interpret, in words, the meaning of this interval.

D.

1. A sample of size 16 is used in testing the null hypothesis that > 100.The sample results indicate that x = 96 and s = 4.Test the null hypothesis using a significance level of .05.

2. What does the significance level tell us?That is, precisely what is it that has a probability of less than .05?Be specific.

E. Suppose you are interested in studying regional differences in crime rates.You take a random sample of 100 cities in the South, and find a mean crime rate of 55 with a sample variance of 5.78.A sample of 100 cities in the North has a mean crime rate of 50 with a sample variance of 6.72.

1. Construct a 95% confidence interval around the difference in crime rates between the population of Southern cities and the population of Northern cities.

2. Interpret, in words, the meaning of this interval.

3. Test the null hypothesis that the mean crime rate for the population of cities in the South is less than (or equal to) the mean crime rate for the population of cities in the North.Use a significance level of .01.

4. In words, what can you say about the relationship between the two variables in this example?(That is, is the relationship statistically significant?).

F. A sociologist is interested in the voting rates of males and females.Two hundred males and two hundred females are randomly sampled.Of these, seventy percent of males and sixty percent of females voted in the last election.

1. Construct a 95% confidence interval around the difference in the proportion of men and women in the population who voted in the last election.

2. Interpret this interval.

3. Test the null hypothesis that, in the population, there is no difference in the proportion of men and women who voted in the last election.Use a significance level of .05.

4. What can you conclude about the relationship between the two variables in this example? (That is, is the relationship statistically significant?).