Answer to Question #275734 in Statistics and Probability for Raseda

Question

A principal at a certain school claims that the students in his school are above average intelligence. A random of thirty (30) students IQ scores have a score of 112. Is there sufficient evidence to support the principal’s claim?

The mean population IQ is μ= 100 with a standard deviation of 15.

Alpha = 0.01

Based on the above data we should

 

       a. not reject H₀.            b. reject H₀.

Answer 1

The hypotheses tested are,

$H_0:\mu=100\space vs \space H_A:\mu\gt 100$

We are given that,

$\bar{x}=112,\space n=30,\space \sigma=15$

The test statistic is given as,

$Z_c=(\bar{x}-\mu)/(\sigma/\sqrt{n})$

$Z_c=(112-100)/(15/\sqrt{30})=12/2.7386=4.3818$

$Z_c$ is compared with the table value at $\alpha=0.01$ given as, $Z_{\alpha}=Z_{0.01}=2.33$.

The null hypothesis is rejected if $Z_c\gt Z_{0.01}.$

Since $Z_c=4.3818\gt Z_{0.01}=2.33,$ we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the students in his school are above average intelligence at 1% level of significance.

The correct answer is b. reject H₀