Question

16. Claim: Less than 55% of people are in favor of labeling foods that contain GMO’s. Test at α = 0.1

Data: 200 people are chosen at random, and 100 of them say they support labeling foods that contain GMO’s.

(a) Are these data statistically significant evidence to support the claim?

(b) Are these data statistically significant evidence to refute the claim?

Answer 1

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

H0: p = 0.55 versus Ha: p < 0.55

This is a lower tailed test.

We are given

Level of significance = α = 0.10

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 100

n = sample size = 200

p̂ = x/n = 100/200 = 0.5

p = 0.55

q = 1 - p = 0.45

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.50 - 0.55)/sqrt(0.55*0.45/200)

Z = -1.4213

Test statistic = -1.4213

P-value = 0.0776

(by using z-table)

P-value < α = 0.10

So, we reject the null hypothesis

There is sufficient evidence to conclude that Less than 55% of people are in favor of labeling foods that contain GMO’s.

(a) Are these data statistically significant evidence to support the claim?

Answer: Yes

(b) Are these data statistically significant evidence to refute the claim?

Answer: No