SOLUTION: Suppose a random sample of 50 values is taken from a normal population with standard deviation 34.7 g. If the sample mean is 167.4 g, construct a 95% confidence interval on the pop

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Question 393770: Suppose a random sample of 50 values is taken from a normal population with standard deviation 34.7 g. If the sample mean is 167.4 g, construct a 95% confidence interval on the population mean.
Suppose a random sample of 5 values is taken from a normal population with standard deviation 34.7 g. If the sample mean is 167.4 g, construct a 95% confidence interval on the population mean
how and why the confidence intervals in problems 4 and 6 are different
Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
ME =1.96[34.7/sqrt(50)] = 9.618
CI: 167.4-9.618 < u < 167.4 + 9.618
CI: 157.78 < u < 177.02
ME =1.96[34.7/sqrt(5)] = 30.416
CI: 136.98 < u < 197.82
confidence intervals in problems 4 and 6 are differ due to sample size
the smaller the sample, the larger the interval is

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Suppose a random sample of 50 values is taken from a normal population with standard deviation 34.7 g. If the sample mean is 167.4 g, construct a 95% confidence interval on the population mean.
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Using a TI-84 I get (157.78,177.02)
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Suppose a random sample of 5 values is taken from a normal population with standard deviation 34.7 g. If the sample mean is 167.4 g, construct a 95% confidence interval on the population mean
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Using a TI-84 I get (136.98,197.82)
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how and why the confidence intervals in problems 4 and 6 are different
The margin of error is different because the standard error of the sample
means is different since 34.7/sqrt(50) is smaller than 34.7/sqrt(5).
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Cheers,
Stan H.