Question

suppose that in a random selection of 100 colored candies, 30% of them are blue. the candy company claims that the percentage of blue candies is equal to 24%. use a 0.01 significance level to test that claim.
the p - value for this hypothesis test is 0.128(round to three decimal places as needed.)
identify the conclusion for this hypothesis test.
○ a. fail to reject ( h_0 ). there is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 24%
○ b. reject ( h_0 ). there is not sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 24%
○ c. reject ( h_0 ). there is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 24%
○ d. fail to reject ( h_0 ). there is not sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 24%

Explanation:

Step1: Determine the decision rule

In hypothesis testing, if the p - value is less than the significance level ($\alpha$), we reject the null hypothesis ($H_0$). Here, $\alpha = 0.01$.

Step2: Analyze each option

• Option A: If we fail to reject $H_0$, we cannot say there is sufficient evidence to reject the claim. So, this option is incorrect.
• Option B: If we reject $H_0$, it means there is sufficient evidence to reject the claim. So, this option is incorrect.
• Option C: If the p - value (not given in full calculation here but assuming the standard process) is less than $\alpha=0.01$, we reject $H_0$. Rejecting $H_0$ implies there is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 24%.
• Option D: If we fail to reject $H_0$, we do not have sufficient evidence to reject the claim. But if the p - value is less than $\alpha$, we should reject. So, this option is incorrect.

Answer:

C. Reject $H_0$. There is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 24%