2026 HCI P2 Q7
2026 HCI P2 Q7
Junior College 2
9 marks
A lighting manufacturer claims that their fluorescent lamps have a population mean lifetime of 9000 hours under standard operating conditions. The quality control team took a random sample of 50 fluorescent lamps and recorded the lifetime. The lifetime, \(x\) hours of the 50 fluorescent lamps are summarised as follows:
\[\sum(x-9000)=-250,\quad\sum(x-9000)^2=36530.\]
- Find the unbiased estimates of the population mean and variance.[2]
- Test at 5% level of significance if the manufacturer has overstated his claim.[5]
- Explain what \(p\)-value means in the context of the question.[1]
- Explain whether using a sample of 15 would have been sufficient for the quality control team to carry out the hypothesis test.[1]
Solution:
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Answer:(a) \(8995\text{ hours}\), \(720\text{ hours}^2\) (b) \(p=0.0938\); do not reject \(H_0\). Insufficient evidence of an overstated claim. (c) Under \(H_0\), probability of a sample mean of 8995 hours or less for 50 lamps. (d) No; population normality is not given and 15 is too small to justify the CLT approximation.
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