A sample of 23 discount brokers showed a sample mean price c

A sample of 23 discount brokers showed a sample mean price charged for a trade of 100 shares at $50 per share was $35.80. Assume a population standard deviation of $5.20. Test the hypothesis that the mean price charged for a tradeof 100 shares at $50 per share is at most $34 at = 0.1

For the hypothesis stated above..

What is the test statistic?

What is the decision?

A) Reject H0

OR

B)Fail to reject H0

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   34  
Ha:    u   <   34  
              
As we can see, this is a    left   tailed test.      
Getting the test statistic, as              
              
X = sample mean =    35.8          
uo = hypothesized mean =    34          
n = sample size =    100          
s = standard deviation =    5.2          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.461538462 [ANSWER, TEST STATISTIC]

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Thus, getting the critical z, as alpha =    0.1   ,      
alpha =    0.1          
zcrit =    -   1.281551566      
              
              
Comparing z > zcrit , we   FAIL TO REJECT THE NULL HYPOTHESIS. [Fail to reject Ho]      
              
There is no significant evidence that the mean price charged for a tradeof 100 shares at $50 per share is at most $34.