Questions: Suppose that in a random selection of 100 colored candies, 25% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%. 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. H0: p=0.29 H1: p>0.29 B. H0: p ≠ 0.29 H1: p=0.29 C. H0: p=0.29 H1: p ≠ 0.29 D. H0: p=0.29 H1: p<0.29 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is . (Round to two decimal places as needed.) Identify the P -value for this hypothesis test.

Solution Steps

We are testing the claim that the percentage of blue candies is equal to \(29\%\). The null and alternative hypotheses are defined as follows:

\[ H_0: p = 0.29 \] \[ H_1: p \neq 0.29 \]

The test statistic for the hypothesis test is calculated using the formula:

\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]

Substituting the values:

• Sample proportion, \(\hat{p} = 0.25\)
• Hypothesized proportion, \(p_0 = 0.29\)
• Sample size, \(n = 100\)

The calculated test statistic is:

\[ Z = -0.8815 \]

The P-value associated with the test statistic \(Z = -0.8815\) is:

\[ \text{P-value} = 0.378 \]

For a significance level of \(\alpha = 0.05\) in a two-tailed test, the critical region is defined as:

\[ Z < -1.96 \quad \text{or} \quad Z > 1.96 \]

Since the calculated test statistic \(Z = -0.8815\) does not fall within the critical region, we fail to reject the null hypothesis.

Final Answer