SOLUTION: According to the norms established for a history test,grade 8 students should have an average 81.7 with a standard deviation of 8.5.If 100 randomly selected grade 8 students from c

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Question 1193651: According to the norms established for a history test,grade 8 students should have an average 81.7 with a standard deviation of 8.5.If 100 randomly selected grade 8 students from certain school district average 79.6 in this test,can we conclude at the 0.05 level of significance that grade 8 students from this school district can be expected to average less than the norm of 81.7?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: mean is 81.7 or higher
Ha: mean is <81.7
alpha=0.05 p{reject Ho|Ho true}
test is a z (0.95)
critical value is z<-1.645
calculation z=diff in mean/SE=-2.1/8.5/sqrt(100)
=-21/8.5=-2.47
reject Ho: there is a significant difference at the 5% level and the population should be considered to have an average less than 81.7
p-value = 0.007, well < 0.05.