2022 RVHS P2 Q10
2022 RVHS P2 Q10
8 marks
Prelims
A mobile application states that the mean time taken to travel from Town A to Park B is \(14.5\) minutes. A data analyst would like to test if the mean travel time is more than \(14.5\) minutes. The data analyst gathers a random sample of \(35\) travel times of various people. The travel times, \(x\) minutes, are summarized below.
\(\sum{x}=539\) \(\sum{{{x}^{2}}}=8647.4\)
- Calculate the unbiased estimates of the population mean and variance of the travel time from Town A to Park B.[2]
- Test, at the \(5\%\) level of significance, whether the mean travel time from Town A to Park B is more than \(14.5\) minutes. You should state your hypotheses clearly and define any symbols used.[4]
- Explain, in the context of the question, the meaning of 'at the \(5\%\) level of significance'.[1]
- Explain, without performing another test, whether the conclusion in part (ii) would have changed if instead the data analyst was testing if the mean travel time from Town A to Park B was not \(14.5\) minutes.[1]
Video Solution:
Video solution locked
A free account saves your progress; this video needs tuition enrolment.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(i) \({\bar{x} = 15.4}\) ; \({s^2 = 10.2}\) (ii) \({p\text{-value} = 0.0477}\) (3 s.f.) As \({p\text{-value} < 0.05}\) , we reject \({H_0}\) . There is sufficient evidence at \({5\%}\) significance level that the mean travel time from Town A to Park B is greater than \({14.5\text{ minutes}}\). (iii) At \({5\%}\) level of significance means there is a probability of \({0.05}\) that the test will conclude that the mean travel time from Town A to Park B is more than \({14.5\text{ minutes}}\) when in fact it is \({14.5\text{ minutes}}\). (iv) \({p\text{-value} = 0.0955}\) (3 s.f.) As \({p\text{-value} > 0.05}\) , the conclusion will change. We conclude that at \({5\%}\) level of significance, there is insufficient evidence that the mean travel time from Town A to Park B is not \({14.5\text{ minutes}}\).
Need help? Join our JC Math tuition classes.
Learn more