A Recent Health of Boston Report Suggests That 14% of Female

question 100

Multiple Choice

A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males. Suppose 250 females and 200 males responded to the study. Which of the following are an appropriate null and alternative hypotheses to test whether the proportion of females suffering from asthma is greater than the proportion of males?

• A) H₀: p₁ − p₂ ≤ 0, H_A: p₁ − p₂ > 0
• B) H₀: p₁ − p₂ ≥ 0, H_A: p₁ − p₂ < 0
• C) H₀: p₁ − p₂ = 0, H_A: p₁ − p₂ ≠ 0
• D) H₀: p₁ − p₂ > 0, H_A: p₁ − p₂ ≤ 0

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Definitions:

Hypothesis Testing

A statistical method that uses sample data to evaluate a hypothesis about a population parameter, leading to a decision to accept or reject the hypothesis.

Test Statistic

A numerical value calculated from a sample of data used in statistical testing to determine whether to reject the null hypothesis.

T-Distribution

A probability distribution used in statistics, especially in scenarios with small sample sizes, that is symmetric, bell-shaped, and slightly thicker and longer-tailed than the normal distribution.

Sample Mean

The average value of a sample set, calculated by summing all observations and dividing by the number of observations.