The instructions are as follows Write all given values State

The instructions are as follows:

-Write all given values

-State the null and alternative hypotheses

-Determine the level of significance,

-Determine the approproiate test statistic to be used and compute

-Determine the critical region and find its value

-Write your decision whether to reject or do not reject the null hypothesis, state your interpretation

The average height of females in the freshman class of a certain college has historically been 162.5 centimeters with a standard deviation of 6.9 centimeters. Is there reason to believe that there has been a change in the average height if a random sample of 50 females in the present freshman class has an average height of 165.2 centimeters? Use 0.05 level of significance. (13pts) 1.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   162.5  
Ha:    u   =/   162.5   [ANSWER, HYPOTHESES]

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As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   [SIGNIFICANCE]

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Getting the test statistic, as              
              
X = sample mean =    165.2          
uo = hypothesized mean =    162.5          
n = sample size =    50          
s = standard deviation =    6.9          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.766939579   [ANSWER, TEST STATISTIC]

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alpha/2 =    0.025          
zcrit =    +/-   1.959963985      
              
Thus, the critical region is z < -1.959963985 or z > 1.959963985. [CRITICAL REGION]

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As z > 1.959963985, we   REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that there is a change in the avergae height of females in the freshman class. [CONCLUSION]