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 23%. use a 0.10 significance level to test that claim. identify the null and alternative hypotheses for this test. choose the correct answer below. a. ( h_{0}: p = 0.23 ) ( h_{1}: p > 0.23 ) b. ( h_{0}: p = 0.23 ) ( h_{1}: p < 0.23 ) c. ( h_{0}: p
eq 0.23 ) ( h_{1}: p = 0.23 ) d. ( h_{0}: p = 0.23 ) ( h_{1}: p
eq 0.23 )

Explanation:

The null hypothesis \(H_0\) is a statement of equality. Here, the company claims \(p = 0.23\), so \(H_0:p = 0.23\). The alternative hypothesis \(H_1\) is what we test against the null. Since we are just testing if the proportion is different from \(0.23\) (a two - tailed test, not specifying greater than or less than in the problem statement about the claim), \(H_1:p
eq0.23\).

Answer:

D. \(H_0: p = 0.23\), \(H_1: p
eq0.23\)