. The weekly mean sales (in thousands of dollars) of the three local hardware st
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Question
. The weekly mean sales (in thousands of dollars) of the three local hardware stores are as shown. Store A: 8.8, 8.3, 9.6, 9.9 Store B: 7.0, 7.9, 5.4, 5.5 Store C: 5.0, 6.2, 4.6, 7.0 Instead of comparing the population weekly mean sales of the three local hardware stores based only on location, suppose we want to compare the mean weekly sales based on location and season of the year (winter, spring, summer, and fall). Which answer represents the correct number of random samples with the goal of having a balanced and crossed design?
Take 12 independent random samples, all of which have equal standard deviations.
Take 4 independent random samples, with 3 observations in each sample.
Take 12 independent random samples, with an equal number of observations in each sample.
Explanation / Answer
For a cross sectional analysis involving 2 factors, we must have observations on every combination of levels of the two factors. Here, we have 2 factors namely the location and season with 3 and 4 levels respectively. Thus, we will have 3×4=12 possible combinations. Also, in order to compare the combinations these observations must have same variance. Hence, we take 12 independent samples with equal standard deviations.
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