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.
the p - value for this hypothesis test is.491
(round to three decimal places as needed.)
identify the conclusion for this hypothesis test.
○ a. reject ( h_0 ). there is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 27%
○ b. fail to reject ( h_0 ). there is sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 27%
○ c. 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 27%
○ d. reject ( h_0 ). there is not sufficient evidence to warrant rejection of the claim that the percentage of blue candies is equal to 27%

Explanation:

To decide on the conclusion of a hypothesis test, we compare the p - value with the significance level ($\alpha$). The rule is: if $p - value\geq\alpha$, we fail to reject the null hypothesis ($H_0$); if $p - value\lt\alpha$, we reject $H_0$. Here, $\alpha = 0.05$ and $p - value=0.491$. Since $0.491\geq0.05$, we fail to reject $H_0$. Failing to reject $H_0$ means there is not enough evidence to reject the claim (the null hypothesis in a proportion test is usually the claim of equality).

Answer:

C. 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 $27\%$