Thirty GPAs from a randomly selected sample of statistics st

Thirty GPAs from a randomly selected sample of statistics students at a college are linked below. Assume that the population distribution is approximately Normal. The technician in charge of records claimed that the population mean GPA for the whole college is 2.88. What is the sample mean? Is it higher or lower than the population mean of 2.88? The chair of the mathematics department claims that statistics students typically have higher GPAs than the typical college student. Use the four-step procedure and the data provided to test this claim. Use a significance level of 0.05. Click the icon to view the data table. What is the sample mean? The sample mean is (Type an integer or decimal rounded to two decimal places as needed.) Is the sample mean higher or lower than the population mean of 2.88? The chair of the mathematics department claims that statistics students typically have higher GPAs than the typical college student. Use the four-step procedure and the data pro

Solution

A)

Getting the mean, X,      
      
X = Sum(x) / n      
Sum(x) =    93.67  

As n = 30,
      
Thus,      
X =    3.122333333   or 3.12 [ANSWER]

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This is HIGHER than the population mean of 2.88. [ANSWER]

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b)

Getting the standard deviation of the sample,

s =    0.367401719

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   2.88  
Ha:    u   >   2.88   [are there other options here?]

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As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    3.122333333          
uo = hypothesized mean =    2.88          
n = sample size =    30          
s = standard deviation =    0.367401719          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.612705822          
              
Also, the p value is              
              
p =    0.000151509          
              
Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.