QCEVault

Statistical inference — Question 10

Original QCE Vault practice · 6 marks

Q10 · Practice questionComplex unfamiliar6 marks

QUESTION 10 (6 marks)

A sensor records a quantity XX. A random sample of 25 readings has sample mean 102.4 and sample standard deviation 3.5.

Use a zz-value of 2 throughout.

a)

Determine an approximate confidence interval for the population mean of XX.

[2 marks]

A calibration converts every reading using Y=0.8X+18Y=0.8X+18.

b)

Determine the sample mean and sample standard deviation of the calibrated readings.

[2 marks]
c)

Determine an approximate confidence interval for the population mean of YY.

[1 mark]
d)

A target value for the calibrated population mean is 100. Comment on whether the sample provides evidence that this target is reasonable.

[1 mark]
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