Question #336064

Assuming that the samples come from normal distributions, find the margin of error E given the following.




2. n=150, x-=98, s=9.90, 95% confidence.



3. n=350, x-=125, s=11.18, 99% confidence.



4. n=500, x-=236, s=15.36, 90% confidence.



5. n=785, x-=459, s=21.42, 99% confidence.

1
Expert's answer
2022-05-05T10:35:36-0400

2. The critical value for α=0.05,df=n1=149\alpha = 0.05,df=n-1=149 degrees of freedom is tc=z1α/2;n1=1.976013.t_c = z_{1-\alpha/2; n-1} = 1.976013.

Margin of Error: E=tc×sn=1.976013×9.9150=1.5973E=t_c\times\dfrac{s}{\sqrt{n}}=1.976013 \times \dfrac{9.9}{\sqrt{150}}= 1.5973


3. The critical value for α=0.01,df=n1=349\alpha = 0.01,df=n-1=349 degrees of freedom is tc=z1α/2;n1=2.58999.t_c = z_{1-\alpha/2; n-1} = 2.58999.

Margin of Error: E=tc×sn=2.58999×11.18350=1.5478E=t_c\times\dfrac{s}{\sqrt{n}}=2.58999\times \dfrac{11.18}{\sqrt{350}}= 1.5478


4. The critical value for α=0.10,df=n1=499\alpha = 0.10,df=n-1=499 degrees of freedom is tc=z1α/2;n1=1.647913.t_c = z_{1-\alpha/2; n-1} = 1.647913.

Margin of Error: E=tc×sn=1.647913×15.36500=1.1320E=t_c\times\dfrac{s}{\sqrt{n}}=1.647913 \times \dfrac{15.36}{\sqrt{500}}=1.1320


5. The critical value for α=0.01,df=n1=784\alpha = 0.01,df=n-1=784 degrees of freedom is tc=z1α/2;n1=2.582115.t_c = z_{1-\alpha/2; n-1} = 2.582115.

Margin of Error: E=tc×sn=2.582115×21.42785=1.9741E=t_c\times\dfrac{s}{\sqrt{n}}=2.582115 \times \dfrac{21.42}{\sqrt{785}}= 1.9741



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