Question

An ABC News poll asked adults whether they felt genetically modified food was safe to eat. 35% felt it was safe, 52% felt it was not safe, and 13% had no opinion.
A random sample of 120 adults was asked the same question at a local county fair. 40 people felt that genetically modified food was safe, 60 felt that it was not safe, and 20 had no opinion.

At the 0.01 level of significance, is there sufficient evidence to conclude that the proportions differ from those reported in the survey?

Answer 1

Answer:

The proportions differ from those reported in the survey.

Step-by-step explanation:

The Chi-square goodness of fit test would be used to determine whether the proportions differ from those reported in the survey.

The hypothesis for the test can be defined as follows:

H₀: The proportions does not differ from those reported in the survey.

Hₐ: The proportions differ from those reported in the survey.

Assume that the significance level of the test is, α = 0.01.

The Chi-square test statistic is given by:

$\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}$

Consider the Excel sheet provided.

The Chi-square test statistic value is 191.32.

The p-value of the test is:

$p-value=P(\chi^{2}_{(n-1)}>191.32)\\\\=\text{CHISQ.DIST.RT}(191.32,2)\\\\=0.0000$

The p-value of the test is very small. The null hypothesis will be rejected at 1% level of significance.

Thus, concluding that the proportions differ from those reported in the survey.