A civil engineer tests the compressive strength psiof a samp

A civil engineer tests the compressive strength (psi)of a sample of 20 concrete blocks. He obtains the following results: Mean = 2230 psi Standard deviation = 38 psi. A minimum psi = 2250 psi is required to use this concrete. Test the hypothesis that the concrete meets this minimum requirement. (alpha = 0.025). What is the critical t-value? What is the calculated t-value? Does this sample support the statement that the mean compressive strength of the concrete is at least 2250 psi?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   2250  
Ha:    u   >   2250  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    19          
tcrit =    +   2.093024054   [ANSWER, CRITICAL T VALUE]

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Getting the test statistic, as              
              
X = sample mean =    2230          
uo = hypothesized mean =    2250          
n = sample size =    20          
s = standard deviation =    38          
              
Thus, t = (X - uo) * sqrt(n) / s =    -2.353755766 [ANSWER, T VALUE]

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As t < 2.093, we FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, we have no sufficient evidence that the concrete\'s mean compressive strength of the concrete is at least 2250 psi. [CONCLUSION]