Printer paper

Topic: Estimation examples · more questions on this topic
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Ten sheets advertised as 100 µm thick measure

97,\;102,\;104,\;96,\;108,\;105,\;101,\;99,\;96,\;102

micrometres. Give a 95% confidence interval for the mean thickness, using t_{9,\,0.975}=2.262. Does the interval suggest the paper is not as advertised?

Worked answer (click to show)

The mean is 101 and the bias-corrected standard deviation is 3.916. Then

101\pm 2.262\times\frac{3.916}{\sqrt{10}}=101\pm 2.80,

which is (98.2,\,103.8), matching (98.1,\,103.9) at the rounding of s. The interval contains 100, so these ten sheets do not show that the mean thickness differs from the advertised value.