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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