QCEVault

Statistical inference — Question 235

Original QCE Vault practice · 7 marks

Q235 · Practice questionTechnology-activeComplex unfamiliar7 marks

QUESTION 235 (7 marks)

A sample of 100 independent observations has x‾=100,s=10\overline x=100,s=10. For an illustrative fitted model, individual future observations have N(100,100)N(100,100) distribution, using variance as the second parameter. Use z=1.96.
a)
Find an approximate 95 percent confidence interval for the unknown population mean.
[2 marks]
b)
Give the central 95 percent range for individuals under the fitted model.
[2 marks]
c)
Find the proportion of fitted individuals within the interval in (a), and explain why the ranges differ.
[3 marks]
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