The fashion chain had isolated two stores that perform under the benchmark of 7.5 (Store 3 and Store 4). Which of the following statements is false?

Question

BlackTom AI · Accepted Answer

First, let’s restate the situation and the options to ensure we’re analyzing the same claim set.
- The scenario mentions that stores 3 and 4 perform under the benchmark of 7.5, indicating underperformance relative to that benchmark.
- We are asked which of the following statements is false.

Option A: 'At the 5% significance level, there is evidence to suggest that Store 4 underperformed.'
- This aligns with the setup that Store 4 is below the benchmark. If a test was performed and 5% significance was used, finding evidence at or below 0.05 would be a typical conclusion for underperformance, assuming the data support a below-7.5 result for Store 4. The statement could be true if the data show a statistically significant drop for Store 4.

Option B: 'At the 5% significance level, there is no evidence to suggest that Store 3 or 4 underperformed.'
- Given the premise that Store 3 and Store 4 are under the benchmark, a claim of no evidence at 5% contradicts the setup. If the stores are indeed underperforming relative to 7.5, one would generally expect some level of evidence against underperformance to be unlikely at the 5% level. This option is inconsistent with the stated condition that these stores underperform, making it a likely false statement.

Option C: 'At the 1% significance level, there is evidence to suggest that Store 4 underperformed.'
- It is plausible that at a more stringent 1% level, Store 4 could still show statistically significant underperformance if the difference from 7.5 is sufficiently large and the sample size supports it. This option could be true if the data yield a p-value below 0.01.

Option D: 'At the 5% significance level, there is evidence to suggest that Store 3 underperformed.'
- Similar to Option A, this is consistent with the premise that Store 3 underperforms relative to the benchmark. If the 5% test rejects the null for Store 3, this statement would be true under typical hypothesis-testing interpretation.

Now, comparing theseities, note how the premise that two stores underperform sets up expectations about evidence at common significance levels. The only option that directly contradicts that premise is the claim that there is no evidence at 5% for either store underperforming, which clashes with the stated underperformance of Stores 3 and 4.

In terms of common statistical reasoning, statements asserting evidence of underperformance (A or D) can be true if the p-values are below 0.05 for the respective store tests. Statement C can also be true if Store 4’s p-value is below 0.01. Statement B, on the other hand, denies any evidence of underperformance at 5% despite the given underperformance, which makes it inconsistent with the setup and thus the false claim among the options.

To summarize the reasoning across options in a natural progression: you assess whether underperformance is compatible with the claimed test significance, check consistency with the benchmark, and evaluate at the specified alpha levels. The option that conflicts with the given condition of underperformance at Stores 3 and 4 is the one that denies evidence at the 5% level, making it the incorrect choice in this question.

MCD2080 - T1 - 2025 Lecture Lesson 1 (week 5)

The fashion chain had isolated two stores that perform under the benchmark of 7.5 (Store 3 and Store 4). Which of the following statements is false?

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MCD2080 - T1 - 2025 Lecture Lesson 1 (week 5)

The fashion chain had isolated two stores that perform under the benchmark of 7.5 (Store 3 and Store 4). Which of the following statements is false?

View Explanation

Log in for full answers

Similar Questions

Which one is true?

For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

For a given sample, the P-value for upper tail test is x, and the P-value for two-tailed test is y, then

For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

For a sample size of 30, changing from using the t distribution to using the standard normal distribution in a hypothesis test _____.

Exhibit 9-5 n = 16 H0: μ ≥ 80 = 75.607 Ha: μ < 80 σ = 8.6 Assume the population is normally distributed. Refer to Exhibit 9-5. The p-value is equal to _____.

Exhibit 9-1 ​ ​ Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter? c08.p089.q0008

More Practical Tools for Students Powered by AI Study Helper

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