Respuesta :
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
[tex]p^{-} = \frac{131}{252} = 0.5198[/tex]
Level of significance = 0.05
Z₀.₀₅ = 1.96
Step:2
95% confidence interval for the proportion of days that IBM stock increases.
[tex](p^{-} - Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p^{-} + Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } )[/tex]
[tex](0.5198 - 1.96(\sqrt{\frac{0.5198(1-0.5198)}{252} } , 0.5198 +1.96(\sqrt{\frac{0.5198(1-0.5198)}{252} })[/tex]
(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)
