You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as .

H0: Mue1-Mue2 less than or equal 0.

Ha: Mue1-Mue2>0

H0: Mue1-Mue greater or equal 0.

Ha: Mue1-Mue<0

H0: P1-P2 less than or equal 0

Ha: P1-P2>0

H0: P1-P2 greater than or 0

Ha: P1-P2<0

H₀: p₁ - p₂ < 0.

Hₐ: p₁ - p₂ > 0.

Step-by-step explanation:

In this case, we need to determine if there is a higher incidence of smoking among women than among men in a neighborhood.

An experiment can be performed involving collecting two samples of men and women and computing the proportion of men and women smokers in the neighborhood. Then these two sample proportions can be used to determine which proportion is higher.

We are computing proportions of men and women smokers instead of the mean number of men and women smokers because the we need to determine the  incidence of smoking among men and women, i.e. the occurrence or frequency or rate of men and women smokers.

So, a two proportion test can be applied to determine whether the proportion of women smokers is higher than men.

The population proportion of women in the neighborhood is represented by p₁ and the  population proportion of men in the neighborhood is represented by p₂.

The hypothesis can be defined as:

H₀: The proportion of women smokers is not higher than men, i.e. p₁ - p₂ < 0.

Hₐ: The proportion of women smokers is higher than men, i.e. p₁ - p₂ > 0.

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