Question

a principal at a school.claims that the students in his school are above average intelligence. A random sample of forty student's IQ score have a mean of 112.5. the mean population IQ is 100 with a standard deviation of 15. use the 5% level of significance.

Answer 1

$H_0:a=100$

$H_1:a>100$

Test statistic: $T={\frac {(112.5-100)*\sqrt{40}} {15}}=5.27$

Since sample size is big, then it is appropriate to use Z-score as critical value, so

$P(Z>Cr)=0.05\implies Cr=1.645$

We can see that T>Cr, so we should reject the null hypothesis and conclude that there is enough statistical evidence to aceept the fact that students IQ is greater than the mean