Question

Genetically modified foods: According to a 2014 Pew Research survey, a majority of the American general public (57%) says that genetically modified (GM) foods are generally unsafe to eat. This month, in a survey of 500 randomly selected American adults, 60% says that GM foods are generally unsafe to eat. We test the hypothesis that the percentage who says that GM foods are generally unsafe to eat is greater than 57% this year. The P-value is 0.088.
Which of the following interpretations of this P-value is valid?

A. Assuming that more than 57% of Americans feel that GM foods are unsafe, the probability that 60% of 500 randomly selected Americans say that GM foods are generally unsafe to eat is 0.088.

B. If we assume that 57% of Americans says that GM foods are generally unsafe to eat, then there is an 8.8% chance that random sample results will show 60% or more who says that GM foods are generally unsafe to eat.

C. There is an 8.8% chance that 57% of Americans says that GM foods are generally unsafe to eat.

Answer 1

Answer:

Option B is correct.

If we assume that 57% of Americans says that GM foods are generally unsafe to eat, then there is an 8.8% chance that random sample results will show 60% or more who says that GM foods are generally unsafe to eat.

Step-by-step explanation:

In Hypothesis testing, p-value helps to show the significance of one's results.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and is always about the absence of significant difference between two variables being compared.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared.

For this question, the null hypothesis is that 57% of Americans say that GM foods are generally unsafe to eat.

H₀: p = 0.57

And the alternative hypothesis would be that more than 57% of Americans say that GM foods are generally unsafe to eat.

Hₐ: p > 0.57

The p-value is actually defined as the probability of obtaining results as extreme as the observed results in the statistical analysis provided that the null hypothesis is true.

For this question , it is evident that the p-value (0.088) is expressing the probability of getting results as extreme as 60% or more Americans saying that GM foods are unsafe to eat provided that the null hypothesis (57% of Americans say that GM foods are generally unsafe to eat) is true.

Hope this Helps!!!