In order to determine whether or not there is a significant

In order to determine whether or not there is a significant difference in the stock-picking ability of two brokerages, we want to use a hypothesis test to compare the annual gain for a $1000 investment.

Firm 1

Firm 2

Sample size                   

30

40

Sample mean                   

264

199

Sample standard deviation     

157

111

Refer to Exhibit A.

Assuming an alpha of 5%, the null hypothesis a. is rejected b. not rejected c. Not enough information is provided to answer this question. d. None of the above answers are correct

Solution

H0: population mean for farm 1 = population mean for farm 2
ag. H1: population mean for farm 1 not equals population mean for farm 2

i.e, H0: mu1- mu2 = 0 ag. H1: mu1 not equal to mu2......

Standard Error = sqrt[ (s₁²/n₁) + (s₂²/n₂) ]

where s₁ is the standard deviation of firm 1, s₂ is the standard deviation of firm 2, n₁ is the size of firm 1, and n₂ is the size of farm 2.

degrre of freedom= DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

Here, s_{1 = 157 ,} n_{1 = 30 ,} s_{2 =111 and} n₂ = 40............

test statistic = (sample mean for firm 1 - sample mean for firm 2 ) / std. error

calculation:

test statistic = 2.0298
  df = 68
  standard error of difference = 32.022

then, p-value for test stat. is = 0.0463

alpha= 0.05

Since the P-value (0.0463) is less than the significance level (0.05) ,we cannot accept the null hypothesis...
a) null hyp is rejected!