Question

A young investor in the stock market is concerned that investing in the stock market is actually​ gambling, since the chance of the stock market going up on any given day is 50​%. She decides to track her favorite industrial company stock for 269 consecutive days and finds that on 145 days the stock was​ "up." Complete parts a through c.

​a) Find a95% confidence interval for the proportion of days the stock is​ "up."

​b) Does your confidence interval provide any evidence that the market is not​ random? Explain.

​c) What is the significance level of this​ test? Explain

Answer 1

a )

Given : x = 145, n = 269, = x/n = 0.5390

confidence level = 0.95, Therefore α = 1 - 0.95 = 0.05 , (α/2) = 0.025

z_0.025 = 1.96 ---- from z score table.

Confidence interval =   

p* (1-p) p/2*1

0.5390 +1.96 * 10.5390 + (1-0.5390 269

So 95% confidence interval for the proportion of days the stock is​ "up" is ( 0.4794 , 0.5986 )

b) confidence interval contain 0.50 , therefore confidence interval does not provide any evidence that the market is not​ random.

C) Significance level α = 0.05