Question

The 92% confidence interval is _______.

Short answer

Lower limit = 0.7217

Upper limit = 0.87830

(0.7217,0.87830).

Step-by-step solution

Given Information

Formula used for the 92% confidence interval is

$CI=P\pm z_c\sqrt{\frac{pq}{n}}$Formula:

Calculation

The 92% confidence interval is given by lower limit,

Lower limit = p'- $z_{aI2}$$\sqrt{\frac{p\text{'}q\text{'}}{n}}$

Lower limit = 0.8- $z_{0.004}$$\sqrt{\frac{0.8(1-0.8}{80}}$

Lower limit = 0.8 - 0.07830472

Lower limit = 0.7217

The 92% confidence interval is given by upper limit,

Upper limit formula is given by,

Upper limit =p'+ $z_{aI2}$$\sqrt{\frac{p\text{'}q\text{'}}{n}}$

Upper limit = 0.8+$z_{0.004}$$\sqrt{\frac{0.8(1-0.8)}{80}}$

Upper limit= 0.8 + 1.751 x 0.04472

Upper limit = 0.8 + 0.07830472

Upper limit = 0.87830

Conclusion

As a result, the 92 percent confidence interval for the true proportion of girls aged 8 to 12 who began ice skating lessons at the ice chalet is calculated as follows: (0.7217, 0.87830).