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 a total of 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 P-value for the test?

Question

Quizplus · Accepted Answer

We want to test whether the proportion of adults who mostly drink either regular or diet soda is greater than 0.50. 
The null hypothesis is that p = 0.50 and the alternative hypothesis is that p > 0.50. 
To conduct the hypothesis test, we can use a one-sample proportion test with a significance level of 0.05. 
The sample proportion of adults who mostly drink either regular or diet soda is 56%, which corresponds to a sample proportion of 0.56. 
The test statistic is: z = (0.56 - 0.50) / sqrt[(0.50)(0.50) / 2027] = 5.33 
Using a standard normal distribution table or calculator, the P-value is less than 0.001. 
Since the P-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the majority of American adults drink mostly either regular or diet soda.

In 2013, Gallup Surveyed a Nationally Representative Sample of 2027