Answer to Question #327744 in Statistics and Probability for Zenablyn

Question #327744

A sample of 100 Grade 9 students’ ages was obtained to estimate the mean age of all Grade 9 students. =16 years and the population variance is 16.1.) What is the point estimate for ?



2.) Find the 95% confidence interval for .



3.) Find the 99% confidence interval for .



4.) What conclusions can you make based on each estimate?



1
Expert's answer
2022-04-13T18:34:03-0400

n=100xˉ=16s2=161:μ^=xˉ=162:(xˉt1+γ2,n1sn,xˉ+t1+γ2,n1sn)=(160.41.9842,16+0.41.9842)==(15.2063,16.7937)3:(xˉt1+γ2,n1sn,xˉ+t1+γ2,n1sn)=(160.42.6264,16+0.42.6264)==(14.9494,17.0506)4:With  95%confidence  the  mean  is  in  (15.2063,16.7937)With  99%confidence  the  mean  is  in  (14.9494,17.0506)n=100\\\bar{x}=16\\s^2=16\\1:\\\hat{\mu}=\bar{x}=16\\2:\\\left( \bar{x}-t_{\frac{1+\gamma}{2},n-1}\frac{s}{\sqrt{n}},\bar{x}+t_{\frac{1+\gamma}{2},n-1}\frac{s}{\sqrt{n}} \right) =\left( 16-0.4\cdot 1.9842,16+0.4\cdot 1.9842 \right) =\\=\left( 15.2063,16.7937 \right) \\3:\\\left( \bar{x}-t_{\frac{1+\gamma}{2},n-1}\frac{s}{\sqrt{n}},\bar{x}+t_{\frac{1+\gamma}{2},n-1}\frac{s}{\sqrt{n}} \right) =\left( 16-0.4\cdot 2.6264,16+0.4\cdot 2.6264 \right) =\\=\left( 14.9494,17.0506 \right) \\4:\\With\,\,95\% confidence\,\,the\,\,mean\,\,is\,\,in\,\,\left( 15.2063,16.7937 \right) \\With\,\,99\% confidence\,\,the\,\,mean\,\,is\,\,in\,\,\left( 14.9494,17.0506 \right)


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