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can you solve this so i can make sure I understand this How many 6 sample means

ID: 3021840 • Letter: C

Question

can you solve this so i can make sure I understand this

How many 6 sample means 80% confidence intervals would need to include the population mean, if the entire population included only 20 items. Confidence interval calculation a foundry run of steel is sampled to ensure the density is meeting customer expectations. 144 samples are taken, they have an average density of 7990kg/m^3 , and a standard deviation of 500kg/m^3 . Determine the 95% confidence interval on that average, and explain what that renge represents.

Explanation / Answer

2.

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    7990          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    500          
n = sample size =    144          
              
Thus,              
Margin of Error E =    81.66516602          
Lower bound =    7908.334834          
Upper bound =    8071.665166          
              
Thus, the confidence interval is              
              
(   7908.334834   ,   8071.665166   )

Thus, we are 95% confident that the true mean density of steel is between 7908.33 kg/m^3 and 8071.665 kg/m^3. [ANSWER]

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