Question

A researcher hypothesizes that the percentage of Ball State University students who sleep 8 or more hours per night is lower than the general population of adults. Previous research has found that 40% of adults sleep 8 hours or more per night. In a recent survey of Ball State students, the researcher found that 38 students reported sleeping 8 hours or more and 82 students reported sleeping less than 8 hours. Do the Ball State student sleep habits differ from those expected of the general population of adults?

a. Using Excel, conduct a Chi-square goodness of fit test on these data.

b. Report the results in a textbox. Be sure to provide both a statistical and research conclusion.

Answer 1

    Research shows 40% of adults sleep 8 hours or more                      
   Thus 60% of adults sleep less than 8 hours                      
   n = 38 + 82 = 120   Number of students studied                  
                          
   Null and alternative hypothesis are                      
   Ho : There is no difference between Ball State student sleep habits and expected of general population                      
   Ha : There is a difference between Ball State student sleep habits and expected of general population                      
                          
   We find the expected frequency by multiplying each probability with total students studied(120)                      

Category	Observed Freq (O)	Expected Freq (E )
8 hours or more sleep	38	48
Less than 8 hours sleep	82	72

a)   Using Excel function chisq.test we get the p-value for the test                      
   p-value = CHISQ.TEST(observed frequencies,   expected frequencies)                      
   p-value = 0.0624                      
   We assume                       
   α = 0.05   that is 5% significance level                  
   0.0624 > 0.05                      
   Since p-value > α, we do not reject the null hypothesis                      
                          
                          
b)   Results                      
                          
   p-value = 0.0624                      
   Decision : Do not Reject the null hypothesis          

          
   Conclusion (Statistical) :                       
   There does not exist sufficient statistical evidence at 5% level of significance                      
   to show that there is a difference between Ball State student sleep habits and expected of general population                      
                          
   Conclusion (Research) :                      
   Ball State student sleep habits do not differ from those expected of the general population of adults