Question

Fit watch ~ Fitness trackers and smart watches with fitness tracking features have become more common over the past few years. In a study done by Gallup in November 2019, out of a random sample of 516 females, 114 wore fitness trackers. In the same study, out of a random sample of 500 males, 78 wore fitness trackers.

We want to estimate the actual difference between the proportions of females and males who wear fitness trackers.

Notation: 1=females and 2=males.

Based on this data, what is the upper bound for a 95% confidence interval for the difference in the population proportions, p1−p2p1-p2

Answer 1

One sided confidence interval :-

(p̂1 - p̂2) ± Z(α) * √( ((p̂1 * q̂1)/ n1) + ((p̂2 * q̂2)/ n2) )

Z(α) = Z(0.05 /2) = 1.645

Upper Limit = ( 0.2209 - 0.156 )+ Z(0.05) * √(((0.2209 * 0.7791 )/ 516 ) + ((0.156 * 0.844 )/ 500 )) = 0.1051

95% confidence interval for  upper bound is 0.1051.