Question

A well know Statistical Institution claims that the average College tuition for a law degree costs at least thirty five thousand dollars. Analyzing a sample of fifty law schools in the vicinity of the study we found the sample had a mean tuition of $33,450 with a population standard deviation of $5,978 per year. At 2% level of significance test the Institution's claim.(Show all work for credit, do not skip any steps)

(a) The hypothesis structure,

(b) The p-value and if you accept or reject the claim (Round the p-value to 4 decimal places)

(c) The conclusion as a verbal statement.

Answer 1

a)

Ho :   µ =   35000  
Ha :   µ <   35000   (Left tail test)
          

b)

Level of Significance ,    α =    0.020  
population std dev ,    σ =    5978.0000  
Sample Size ,   n =    50  
Sample Mean,    x̅ =   33450.0000  
          
'   '   '  
          
Standard Error , SE = σ/√n =   5978/√50=   845.4169  
Z-test statistic= (x̅ - µ )/SE =    (33450-35000)/845.4169=   -1.833  
          
          
p-Value   =   0.0334   [ Excel formula =NORMSDIST(z) ]

Decision:   p-value>α, Do not reject null hypothesis

.................

Please let me know in case of any doubt.

Thanks in advance!

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