Question

Suppose that in a random selection of 100 colored​ candies, 22​% of them are blue. The candy company claims that the percentage of blue candies is equal to 25​%. Use a 0.10 significance level to test that claim.

Answer 1

H₀: P = 0.25

H₁: P 0.25

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                             = (0.22 - 0.25)/sqrt(0.25 * (1 - 0.25)/100)

                             = -0.69

At 0.10 significance level, the critical values are z_0.05 = +/- 1.645

Since the test statistic value is not less than the negative critical value(-0.69 > -1.645), so we should not reject the null hypothesis.

At 0.10 significance level, there is sufficient evidence to support the claim that the percentage of blue candies is equal to 25%.