Question

suppose that in a random selection of 100 colored candies, 24% of them are blue. the candy company claims that the percentage of blue candies is equal to 27%. use a 0.05 significance level to test that claim.

identify the null and alternative hypotheses for this test. choose the correct answer below.

○ a. ( h_0: p
eq0.27 )
( h_1: p = 0.27 )

○ b. ( h_0: p = 0.27 )
( h_1: p
eq0.27 )

○ c. ( h_0: p = 0.27 )
( h_1: plt0.27 )

○ d. ( h_0: p = 0.27 )
( h_1: pgt0.27 )

Explanation:

The null hypothesis \(H_0\) is a statement of equality. Here, the company claims that the proportion \(p = 0.27\), so \(H_0:p = 0.27\). The alternative hypothesis \(H_1\) is what we test against the null. Since we are just testing if the claimed proportion is incorrect (not specifically if it is less than or greater than), it is a two - tailed test. So \(H_1:p
eq0.27\).

Answer:

B. \(H_0: p = 0.27\), \(H_1: p
eq0.27\)