SOLUTION: A friend who hears that you are taking a statistics course asks for help with a specific chemistry lab report. She has made four independent measurements of the specific gravity o

Question 217596: A friend who hears that you are taking a statistics course asks for help with a specific chemistry lab report. She has made four independent measurements of the specific gravity of a compound. The results are: 3.96, 4.38, 3.69 and 4.38. You are willing to assume that the measurements are not biased. This means that the mean μ of the distribution of measurements is the true specific gravity.
a. Calculate a 95% confidence interval for the true specific gravity for your friend.
b. Explain to your friend what this means.
c. What must be true about your friend�s measurements for your results in part (a) to be correct?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A friend who hears that you are taking a statistics course asks for help with a specific chemistry lab report. She has made four independent measurements of the specific gravity of a compound. The results are: 3.96, 4.38, 3.69 and 4.38. You are willing to assume that the measurements are not biased. This means that the mean μ of the distribution of measurements is the true specific gravity.
a. Calculate a 95% confidence interval for the true specific gravity for your friend.
sample mean = 4.10 ; sample standard deviation = 0.339
InvT(0.975,3) = 3.182
standard error: 3.182[0.339/sqrt(4)] = 0.539
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95% CI: 4.10-0.539 < u < 4.10+0.539
95% CI: 3.56 < u < 4.64
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b. Explain to your friend what this means.
We are 95% confident that the mean of measurements of the specific gravity
is between 3.56 and 4.64
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c. What must be true about your friend�s measurements for your results in part (a) to be correct? They must be random and accurate.
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Cheers,
Stan H.

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