SOLUTION: The average Intelligent Quotient (IQ) of the adult population is 100. A researcher believes the average IQ of adults is lower. A random sample of 5 adults are tested and scored.69,

Click here to see ALL problems on Probability-and-statistics

Question 1183486: The average Intelligent Quotient (IQ) of the adult population is 100. A researcher believes the average IQ of adults is lower. A random sample of 5 adults are tested and scored.69,79,89,99,109 and standard deviation 15.81. Is there enough evidence to suggest the average IQ is lower?
Found 2 solutions by Boreal, robertb:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Assuming random and normal distribution
this is a one-way one sample t-test
t(0.975,df=4) with critical value of 2.132
t=(xbar-mean)/s/sqrt(n)
mean is 89
t=(89-100)/15.81/sqrt(5)
=11 sqrt(5)/15.81=1.56
insufficient evidence to reject Ho, p-value is 0.097

Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website!

When significance level is unspecified it is normally assumed to be 5%, or 0.05.

From stattrek.com, p-value = for t-distribution with 4 d.f.
Since , do not reject the null hypothesis and there is no reason to believe that average IQ is lower than 100.