Answer to Question #187551 in Statistics and Probability for Mishal

Question #187551

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.


1
Expert's answer
2021-05-07T10:01:46-0400

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.


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