Consider a scenario where we analyze the pricing behavior of

Consider a scenario where we analyze the pricing behavior of two common shares (one in XYZ corporation and one in MIM corporation). We have collected daily price changes for both stocks for the last 100 trading days. The average daily price change in the stock of XYZ corporation during that time period is $0.06 with the population standard deviation of $0.10. The stock of MIM corporation has the sample average daily price change of $0.03 and the population standard deviation of $0.09. Based on this information, can we conclude that the two stocks exhibit equal average daily growth rates? Please conduct a 90% confidence test to investigate the hypothesis that the two average daily price changes are equal. PLEASE ASSUME THAT THE TWO standard deviations listed here are the POPULATION standard deviations.

Question 3 options:

A) Fail to reject the null that both means are equal.

B) Reject the null that both means are equal.

C) None of the above as not enough information is provided.

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Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.1          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    0.06          
X2 =    0.09          
              
Calculating the standard deviations of each group,              
              
s1 =    0.1          
s2 =    0.09          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    100          
n2 = sample size of group 2 =    100          

Also, sD =    0.013453624          
              
Thus, the t statistic will be              
              
z = [X1 - X2 - uD]/sD =    -2.229882439          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for z is              
              
zcrit =    +/-1.644853627
      
[=NORMSINV(0.05) will give you this]
              
As |z| > 1.6449, then we reject Ho.

OPTION B: Reject the null that both means are equal. [ANSWER]