The fashion chain had isolated two stores; one that performed well (Store 2) and one store that performed under the benchmark of 7.5 (Store 4). Store 4 claims that their average score is smaller due to larger variation in their sample. The survey statistics are summarised below: Which of the following statements is FALSE?

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BlackTom AI · Accepted Answer

To assess the statements, I will examine the 95% confidence intervals (CIs) shown for Store 2 and Store 4, and relate them to the benchmark.
Option a: The 95% CI for Store 2 is from 7.643 to 8.144. Since 7.5 lies below this interval, the benchmark of 7.5 is not contained in Store 2's CI. This implies Store 2 has likely outperformed the benchmark. Therefore, option a is accurate.
Option b: The 95% CI for Store 4 is from 6.632 to 7.315. The benchmark value of 7.5 lies above this interval, so 7.5 is indeed outside Store 4's CI. This means Store 4 did not reach the benchmark according to this interval, so option b is also accurate.
Option c: The statement says '5% of the intervals for Store 4 contain the true average score.' A 95% CI is constructed so that about 95% of such intervals would contain the true mean if the sampling process were repeated many times. Consequently, only about 5% of intervals would fail to contain the true mean, not contain it. Thus this statement is false.
Option d: Since Store 2's CI (7.643–8.144) and Store 4's CI (6.632–7.315) do not overlap, there is statistical evidence suggesting a difference between the stores, with Store 2 performing better than Store 4. Therefore option d is true.
Overall, the analysis shows that only option c makes a false claim about the confidence-interval behavior, while the others are consistent with the intervals provided and the benchmark.

MCD2080 - T1 - 2025 Lecture Lesson 1 (week 4)

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