In a recent survey of gun control laws, a random sample of 1000 women showed that 65% were in favor of stricter gun control laws. In a random sample of 1000 men, 60% favored stricter gun control laws. Construct a
95% confidence interval for $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$
A)(0.008, 0.092)
B)(0.587, 0.912)
C)(-1.423, 1.432)
D)(-2.153, 1.679)

Question

Quizplus · Accepted Answer

The confidence interval for the difference between two proportions ($p_1 - p_2$) can be calculated using the formula for the standard error of the difference between two proportions and the Z-score for the desired confidence level (95% in this case, which corresponds to a Z-score of approximately 1.96). The calculation involves the sample proportions (0.65 for women and 0.60 for men), the sample sizes (1000 for both), and the formula for the confidence interval. The result (0.008, 0.092) falls within the range of option A, indicating a small but positive difference in the proportion of women versus men who favor stricter gun control laws.

In a Recent Survey of Gun Control Laws, a Random p1−p2\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }p1​−p2​

In a Recent Survey of Gun Control Laws, a Random $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$