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Statistical inference — Question 150

Original QCE Vault practice · 1 mark

Q150 · Practice questionTechnology-activeComplex familiar1 mark

QUESTION 150

An instrument records Y=1.2X+0.6Y=1.2X+0.6, where XX is the true measurement and YY is the recorded measurement, both in millimetres. This calibration relationship is exact.
A random sample of 64 independent measurements has recorded sample mean y‾=18.6\overline y=18.6 and recorded sample standard deviation sY=2.4s_Y=2.4. Assume the conditions for an approximate normal confidence interval are satisfied.
Using z=1.96z=1.96, which interval is the approximate 95% confidence interval for the population mean of the true measurement XX?
(A)
(18.012, 19.188) mm(18.012,\ 19.188)\ \mathrm{mm}
(B)
(14.510, 15.490) mm(14.510,\ 15.490)\ \mathrm{mm}
(C)
(14.412, 15.588) mm(14.412,\ 15.588)\ \mathrm{mm}
(D)
(14.93875, 15.06125) mm(14.93875,\ 15.06125)\ \mathrm{mm}
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