4 The Dow jones Industrial Average closing price for the hul

4. The Dow jones Industrial Average closing price for the hull market In 1982 - 1986 is shown below: The question hero is that can we conclude that the Dow jones index is more likely to move higher during bull market? We select 1112 trading days and find out that 573 days that the actual Dow Jones index increased. Suppose we write the hypothesis as the follows: H0:p = 0.5 H1:p > 0.5 Write down the procedure and conclusions In such hypothesis testing using level of significance 0.05.

Solution

H0: p=0.5 ag,. H1: p > 0.5...
sample proportion = 573 / 1112 = 0.5153....
population standard error =sqrt( 0.5 * 0.5 / 1112 ) = 0.015..

Now, test statistic = (0.5153- 0.5) / 0.015 = 1.02..
p-value =  0.1538642
so, p-value is > 0.05 i.e the significance level!
Hence,we accept H0 and claim that p is 0.5...