You randomly select a group of 100 UIC students to take your

You randomly select a group of 100 UIC students to take your survey, and 61 students fill it out. You calculate the average HOS scores to be mean(point estimate)=40.39 and standard deviation=22.04. You learn that the XYZ Humor Institute has surveyed college students across the US, and found their average HOS scores are 39.3. Do we have enough evidence to say whether UIC students have a higher humor orientation than students in the rest of the country? Use a significant level of 5% to test you assumptions, and be sure to show all of the steps of your analysis (state the hypotheses, calculate the test statistic, find the probability, state the conclusion). Be sure to explain why you reached your conclusion.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   39.3  
Ha:    u   >   39.3  
              
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 =    40.39          
uo = hypothesized mean =    39.3          
n = sample size =    61          
s = standard deviation =    22.04          
              
Thus, z = (X - uo) * sqrt(n) / s =    0.386260079 [ANSWER, TEST STATISIC]          
              
Also, the p value is              
              
p =    0.349652031   [ANSWER, P VALUE]      
              
As z < 1.645, and P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence to say that UIC students have a higher humor orientation than students in the rest of the country. [CONCLUSION]