Use Technology and a ttest to test the claim about the popul

Use Technology and a t-test to test the claim about the population mean u at the given level of significance a using the given sample statistics . Assume the population is normally distributed. Claim: u>78; a=0.01 Sample statistics: x= 78.4, s=3.5 n=28

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   78  
Ha:    u   >   78  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    27          
tcrit =    +   2.472659912      
              
Getting the test statistic, as              
              
X = sample mean =    78.4          
uo = hypothesized mean =    78          
n = sample size =    28          
s = standard deviation =    3.5          
              
Thus, t = (X - uo) * sqrt(n) / s =    0.604743157          
              
Also, the p value is              
              
p =    0.275199307          
              
As p > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that the population mean is greater than 78. [CONCLUSION]