Question

An ABC News poll asked adults whether they felt genetically modified food was safe to eat. Thirty-five percent 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. Forty 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 poll?

Work must include functions used on TI 84+ calculator.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: The proportion does not differ from those reported in the poll.

Alternative hypothesis: The proportion differs from those reported in the poll.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 3 - 1
D.F = 2
(E_i) = n * p_i

X² = 1.43

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, E_i is the expected frequency count for level i, O_i is the observed frequency count for level i, and X² is the chi-square test statistic.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 1.43.

We use the Chi-Square Distribution Calculator to find P(X² > 1.43) = 0.489

Interpret results. Since the P-value (0.489) is greater than the significance level (0.05), we failed to reject the null hypothesis.

At the 0.01 level of significance, we do not have sufficient evidence to conclude that the proportions differ from those reported in the poll.

Steps for Ti 84+

1) Click 2nd < Stat < Edit < For L1 - enter observed value and L2 - enter expected value.

2) Click STAT < Tests < X²-GOF test.

3) Enter L1 as Observed, L2 as expected.

4) Enter n -1 as d.f

5) Now click on Calculate.

Observed Expected Safe 40 42.00 0.095238095 Not safe 62.40 0.092307692 No opinion 15.60 1.241025641 200 120 120 1.428571429 Total

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