The time, in minutes, spent by customers at a particular gym has the distribution $$\(\mathrm{N}(\mu, 38.2)\)$$. In the past the value of $$\(\mu\)$$ has been 42.4. Following the installation of some new equipment the management wishes to test whether the value of $$\(\mu\)$$ has changed. The mean time for a sample of 20 customers is found to be $$\(45.6\)$$ minutes. Test at the $$\(2.5 \%\)$$ significance level whether the value of $$\(\mu\)$$ has changed. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_62 Year：2021 Question No：5(b)
Answer:
\(\mathrm{H}_{0}\) : population mean (or \(\mu\) ) \(=42.4\)
\(\mathrm{H}_{1}\) : population mean (or \(\mu\) )\( \neq {42.4} \)
\( \pm \frac{45.6-42.4}{\sqrt{\frac{38.2}{20}}} \)
± 2.315
2.240 < ‘2.315’
There is evidence that \(\mu\) or mean time has changed
\(\mathrm{H}_{1}\) : population mean (or \(\mu\) )\( \neq {42.4} \)
\( \pm \frac{45.6-42.4}{\sqrt{\frac{38.2}{20}}} \)
± 2.315
2.240 < ‘2.315’
There is evidence that \(\mu\) or mean time has changed
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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