Answer to Question #286990 in Physics for Kavyashree

Question

A school principle claims that the students in his school are above average intelligence. A random sample of 30 studets IQ scores have mean of 112.5.Is there sufficient evidence to support the principals claim?The mean population IQ is 100 with standard deviation of 1.5

Answer 1

Let's find z-value:

$$z = \dfrac{x-x_{mean}}{\sigma/\sqrt{n}}$$

where $\sigma = 1.5, n=30, x=112.5, x_{mean}=100$. Thus, obtain:

$$z = \dfrac{112.5-100}{1.5/\sqrt{30}} \approx 45.6$$

This value is much greater than the critical values of $z$, thus, the evidence is sufficient to support the principals claim.

Answer. The evidence is sufficient to support the principals claim.