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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