Answer to Question #211847 in Statistics and Probability for Melenia Mae Dela R

Question

Problem 1.

A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112.5. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15. Use 0.01 level of significance.

Answer 1

$\mu=100$

$\sigma=15$

$\bar X=112.5$

$n=30$

$\alpha=0.01$

$H0:\mu=100$

$Ha:\mu>100$

$z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z=\frac{112.5-100}{\frac{15}{\sqrt{30}}}=4.56$

$CV=z_{0.99}=2.33$

Since the test statistic 4.56 is greater than the critical value 2.33, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the students in his school are above average intelligence.