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.
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.
Comments
Leave a comment