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

Answer:

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

(0.45814 , 0.58146)

Step-by-step 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

                      $p^{-} = \frac{131}{252} = 0.5198$

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step:2

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

$(p^{-} - Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p^{-} + Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } )$

$(0.5198 - 1.96(\sqrt{\frac{0.5198(1-0.5198)}{252} } , 0.5198 +1.96(\sqrt{\frac{0.5198(1-0.5198)}{252} })$

(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)