Question

Gender and Gun Control A survey reported in Time magazine included the question "Do you favor a federal law requiring a 15 day waiting period to purchase a gun?" Results from a random sample of US citizens showed that 318 of the 520 men who were surveyed supported this proposed law while 379 of the 460 women sampled said "yes". Use this information to find and interpret a \(90 \%\) confidence interval for the difference in the proportions of men and women who agree with this proposed law.

Short answer

The 90% confidence interval for the difference in proportions of men and women supporting the 15-day waiting period law to purchase a gun would be calculated using the above steps. The interval would indicate the range in which we're 90% confident that the true difference in population proportions lies.

Step-by-step solution

Calculate the proportions

To begin with, we need to calculate the proportions of males and females that support the law. This is done by dividing the number of people that agree with the proposition by the total number. Let's denote \(p_1\) as proportion of males supporting the law and \(p_2\) as proportion of females supporting the law.\n\nCompute \(p_1 = \frac{318}{520}\) and \(p_2 = \frac{379}{460}\).

Compute the Difference in Proportions

The difference in proportions is computed as \(\delta = p_1 - p_2\). Calculate \(\delta\).

Calculate the Standard Error

The standard error (SE) for the difference in proportions is calculated using the formula \n\n\[SE = \sqrt{ \frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2} }\] \n\nwhere \(n_1\) and \(n_2\) are the number of males and females surveyed. Compute the SE.

Use the Z-table

For our 90% confidence interval, the corresponding z-value is 1.645. Look up this value in a z table or use software to find it.

Calculate the Confidence Interval

The confidence interval is calculated as \(\delta \pm z * SE\). Compute the lower and upper bounds of the interval.