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Statistical inference — Question 286

Original QCE Vault practice · 6 marks

Q286 · Practice questionTechnology-activeComplex unfamiliar6 marks

QUESTION 286 (6 marks)

Two independent studies each use n=100. Their observed 95% confidence intervals are (18,22)(18,22) and (23,29)(23,29). Both use x‾±1.96s/n\overline x\pm1.96s/\sqrt n. The confidence level is changed using the same two datasets.
a)
Determine the two observed means and standard deviations.
[2 marks]
b)
Determine the common confidence level at which the upper endpoint of the first interval first equals the lower endpoint of the second. Give one decimal place.
[3 marks]
c)
Explain why the touching point is not, by itself, an estimate based on a pooled dataset.
[1 mark]
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