Sorting-time conclusions from an inconclusive test

Sorting-time conclusions from an inconclusive test

Junior College 2
4 marks

A parcel company claims that the population mean time taken by its automated system to sort a parcel is less than \(42\) seconds. A one-tailed test is carried out. At the \(6\%\) significance level, it is found that there is insufficient evidence that the population mean sorting time is less than \(42\) seconds. Using only this information, and giving a reason in each case, state whether each of the following statements is (i) necessarily true, (ii) necessarily false, or (iii) neither necessarily true nor false.

  1. There is significant evidence at the \(2\%\) significance level that the population mean sorting time is less than \(42\) seconds.

    [2]
  2. There is significant evidence at the \(10\%\) significance level that the population mean sorting time is less than \(42\) seconds.

    [2]

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Answer:(a) Necessarily false (b) Neither necessarily true nor false

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