In 2013, Gallup surveyed a nationally representative sample of 2027 adults about their soda consumption. The survey showed that 24% mostly drank diet soda. This survey also found that 56% drank mostly either regular or diet soda. Is this evidence that the majority of American adults drink mostly either regular or diet soda? To answer this question, you test the following hypotheses:
H₀: p = 0.50, H_a: p > 0.50
What is the z test statistic for this test?

Question

Quizplus · Accepted Answer

The z test statistic is calculated using the formula for a proportion: z = (p̂ - p0) / √(p0(1-p0)/n), where p̂ = 0.56, p0 = 0.50, and n = 2027. Plugging in these values gives z = (0.56 - 0.50) / √(0.50*0.50/2027) = 5.40.

In 2013, Gallup Surveyed a Nationally Representative Sample of 2027