Question

A stock market analyst notices that in a certain year, the price of IBM stock increased on 131 out of 252 trading days. Can these data be used to find a 95% confidence interval for the proportion of days that IBM stock increases

Answer 1

95% confidence interval for the proportion of days that IBM stock increases.

(0.45814 , 0.58146)

Explanation:

Step:1

Given that a stock market analyst notices that in a certain year, the price of IBM stock increased on 131 out of 252 trading days.

Given that the sample proportion

`p^(-) = (131)/(252) = 0.5198`

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step:2

95% confidence interval for the proportion of days that IBM stock increases.

`(p^(-) - Z_(0.05) (√(p(1-p)) )/(√(n) ) , p^(-) + Z_(0.05) (√(p(1-p)) )/(√(n) ) )`

`(0.5198 - 1.96(\sqrt{(0.5198(1-0.5198))/(252) } , 0.5198 +1.96(\sqrt{(0.5198(1-0.5198))/(252) })`

(0.5198 - 0.06166 , 0.5198+0.06166)

(0.45814 , 0.58146)

Final answer:-

95% confidence interval for the proportion of days that IBM stock increases.

(0.45814 , 0.58146)