In June 2013, the mayor of New York City proposed a limit of at most 16 ounces o

Question

In June 2013, the mayor of New York City proposed a limit of at most 16 ounces on sugary beverages sold in restaurants. He argued that limiting sugar intake would lower rates of obesity and diabetes.   A Gallup poll used a random sample of 1016 US adults on June 15-16. They asked if people support a ban on sugary beverages with over 16 ounces in restaurants. Only 486 respondents said they favored the ban.

a.) Compute the standardized statistic. Must show your work to receive any credit! (1pt)

b) Use the web app to find the p-value using the theory-based approach. (1pt)

c.) Give your conclusion in the context of the problem.

d.) Is the theory-based approach valid in this situation? Explain why or why not.

Explanation / Answer

a. From given information, number of trials, n=1016, number of events, x=486, therefore, sample proportion, phat=486/1016=0.4783, assume hypothesized proportion, p=0.5. Compute 1-proportion Z test statistic by substituting the given values.

Z=(phat-p)/sqrt[p(1-p)/n]

=(0.4783-0.5)/sqrt[0.5(1-0.5)/1016]

=-1.38

b. The p value: 0.0837

c. The p value is less than assumed significance level, alpha=0.05. Therefore, fail to reject H0. There is not sufficient sample evidence that the proportion of US adults supporting a ban on sugary beverage with over 16 ounces is more than 50%.

d. The Gallup poll used random samples, where, both np=1016*0.5=508, and n(1-p)=1016*0.5=508 are far off from 5. Therefore, the approach is valid.

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