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Answer :
In this scenario, we are dealing with a statistical hypothesis test about the average (mean) weight of a checked bag based on a claim reported by an airline industry trade journal.
To determine whether the average weight is actually what the journal claims, we need to set up two hypotheses:
Null Hypothesis (H₀):
The null hypothesis is a statement that there is no effect or no difference, and it assumes that the status quo is true. In this case, the null hypothesis asserts that the average weight of a checked bag is exactly 37.9 lbs.
Mathematically, it is stated as:
[tex]H_0: \mu = 37.9 \text{ lbs}[/tex]
Alternative Hypothesis (H₁):
The alternative hypothesis is what you might believe to be true or hope to prove. It challenges the null hypothesis. Here, the alternative hypothesis suggests that the average weight of a checked bag is not 37.9 lbs.
Mathematically, it is stated as:
[tex]H_1: \mu \neq 37.9 \text{ lbs}[/tex]
These hypotheses are vital in testing whether any observed differences in a sample are significant or just due to random variance. \n
Why: You test these hypotheses to determine if the journal's reported figure accurately reflects reality or if there's a discrepancy.
How: You would typically conduct a test, such as a t-test or z-test, using sample data you’ve collected on the weight of checked bags to compute a test statistic. You then compare this statistic to a critical value or use it to compute a p-value, which helps you decide whether to reject the null hypothesis in favor of the alternative hypothesis.
By testing these hypotheses, you can statistically infer if the average weight claimed by the journal is an accurate representation of the population.
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