Answer to Question #210381 in Statistics and Probability for donn

Question

a research report that the average iq level of students in philiipines science highschool is 110 a sample of 20 students has a mean iq level of 106 woth a standard deviaton of 9

Answer 1

$\mu = 110 \\ n=20 \\ \bar{x}=106 \\ s=9 \\ H_0: \mu= 110 \\ H_1: \mu≠110$

When n<30 and $\sigma$ is unknown a one sample t-test is used.

$t= \frac{\bar{x}- \mu}{s/ \sqrt{n}} \\ t = \frac{106-110}{9 / \sqrt{20}}= -1.987 \\ df=n-1=20-1=19 \\$

Let use α=0.05

Two-tailed test

$t_{α/2,df} = t_{0.025, 19}=2.093$

If test statistics $|t| > t_{α/2,n-1}$ , you have sufficient evidence to reject H₀.

$|t|=1.987 < t_{0.025, 11}=2.093$

Accept H₀.

There is enough evidence to conclude that the average iq level of students in philippines science highschool is 110 at the 0.05 significance level.