Answer to Question #187640 in Statistics and Probability for Ella Ssebulime

Question #187640

The National Center for Education Statistics surveyed 4400 college graduates about the lengths of time

required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68

years. Based on the above information, construct a 95% confidence interval for the mean time required to

earn a bachelor’s degree by all college students.

The confidence level is ________________%

 


1
Expert's answer
2021-05-07T10:02:55-0400

"n=4400, \\mu=5.15 \\text{ years }, \\sigma=1.68 \\text{ years}"


"\\alpha=0.05,\\dfrac{\\alpha}{2}=0.025"


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


95% confidence level is given by-

"=\\mu\\pm Z_{0.025}\\dfrac{\\sigma}{\\sqrt{n}}"


"=5.15\\pm 1.96\\times \\dfrac{1.68}{\\sqrt{4400}}"


"=5.15\\pm 0.0496"

"=(5.10,5.1996)"


Hence 95% confidence level is (5.10,5.1996)


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