Question

16. Claim: More than 70% of people are in favor of labeling foods that contain GMO’s. Test at α = 0.05 Data: 120 people are chosen at random, and 90 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

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.72

Ha : p > 0.72

n =120

x = 90

= x / n = 90 / 120 = 0.75

P0 = 0.72

1 - P0 = 1 - 0.72 =0.28

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.75 -0.72 / [(0.72*0.28) /120 ]

= 0.73

Test statistic = z = 0.73

P(z >0.73 ) = 1 - P(z < 0.73 ) = 1 - 0.7673

P-value = 0.2327

= 0.05

P-value >

0.2327 >0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that

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