Question

The IQ’s of the college students are known to be normally distributed with mean

of 123. A random sample of 49 students showed an average of IQ 120.67 and

standard deviation 8.44. Test the hypothesis that μ=123 against the alternative that

it is less. Let α=0.05.

Answer 1

Let, $H_o:\mu=\mu_o=123$

and $H_a:\mu<\mu_o$

Given, $n=49, x=120.67,\sigma=8.44$

$Z_{\frac{\alpha}{2}}=Z_{0.025}=1.96$

Then, $x= \mu\pm Z_{\frac{\alpha}{2}}\dfrac{\sigma}{\sqrt{n}}$

$\mu=x+Z_{\frac{\alpha}{2}}\dfrac{\sigma}{\sqrt{n}}$

$=120.67+1.96\times \dfrac{8.44}{\sqrt{49}}$

$=120.67+2.3605=123.01$

Conclusion: As calculated mean $\mu=\mu_o$ . Hence Null Hypothesis is accepted.