Construct the indicated confidence interval for the difference between population proportions p1 - p2. Assume that the samples are independent and that they have been randomly selected.
-x1=65,n1=90 and x2=79,n2=116,construct a 98% confidence interival for the difference berween
population proportions $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$.
A) $- 0.084

Question

Construct the indicated confidence interval for the difference between population proportions p1 - p2. Assume that the samples are independent and that they have been randomly selected.
-x1=65,n1=90 and x2=79,n2=116,construct a 98% confidence interival for the difference berween
population proportions $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$.
A) $- 0.084 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.848$
B) $- 0.108 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.190$
C) $0.596 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.848$
D) $0.572 < p _ { 1 } - p _ { 2 } < 0.872$

Quizplus · Accepted Answer

To construct a 98% confidence interval for the difference between population proportions $p_1 - p_2$, we first calculate the sample proportions: $p_1 = \frac{x_1}{n_1} = \frac{65}{90}$ and $p_2 = \frac{x_2}{n_2} = \frac{79}{116}$. Then, we use the formula for the confidence interval for the difference between two proportions, which includes the critical value for the desired confidence level (which can be found using a Z-table for 98% confidence), the sample proportions, and the sample sizes. The correct calculation leads to the interval $-0.108 < p_1 - p_2 < 0.190$, indicating that choice B is correct.

Construct the Indicated Confidence Interval for the Difference Between Population p1−p2\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }p1​−p2​

Construct the Indicated Confidence Interval for the Difference Between Population $\mathrm { p } _ { 1 } - \mathrm { p } _ { 2 }$