In the past, the time, in hours, for a particular train journey has had mean $$\(1.40\)$$ and standard deviation 0.12. Following the introduction of some new signals, it is required to test whether the mean journey time has decreased. The mean time for a random sample of 50 journeys is found to be $$\(1.36\)$$ hours. Assuming that the standard deviation of journey times is still $$\(0.12\)$$ hours, test at the $$\(2.5 \%\)$$ significance level whether the population mean journey time has decreased. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_63 Year：2021 Question No：2(b)
Answer:
\(\mathrm{H}_{0}\) : Pop mean (or \(\mu\) ) \(=1.4\)
\(\mathrm{H}_{1}\) : Pop mean \((\) or \(\mu)<1.4\)
\(\frac{1.36-1.4}{\frac{0.12}{\sqrt{50}}}\)
\(-2.357\) or \(-2.36\)
\(-2.357<-1.96\) or \(0.0092<0.025\) or \(0.9908>0.975\)
Or CV method \(1.36<1.367\)
There is evidence that (mean) (journey) times have decreased
\(\mathrm{H}_{1}\) : Pop mean \((\) or \(\mu)<1.4\)
\(\frac{1.36-1.4}{\frac{0.12}{\sqrt{50}}}\)
\(-2.357\) or \(-2.36\)
\(-2.357<-1.96\) or \(0.0092<0.025\) or \(0.9908>0.975\)
Or CV method \(1.36<1.367\)
There is evidence that (mean) (journey) times have decreased
Knowledge points:
6.5.3 formulate hypotheses and carry out a hypothesis test concerning the population mean in cases where the population is normally distributed with known variance or where a large sample is used
Solution:
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