Conduct the hypothesis test and provide the test statistic, critical value and P

Question

Conduct the hypothesis test and provide the test statistic, critical value and P-value, and state the conclusion. A package of 100 candies are distributed with the following color percentages: 14% red, 22% orange, 16% yellow 12% brown, 22% blue, and 14% green. Use the given sample data to test the claim that the color distribution is as claimed. Use a 0.01 significance level. Click the icon to view the color counts for the candy in the package. The test statistic is (Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer parts Clear All Check Answer

Explanation / Answer

We need the actual data for multiple packages as the sample data (as mentioned in the question). But, it is unavailable to us here. Please comment back with the sample data on this solution.

--------------- ASSUMING: we have the mentioned sample data ----------------

The sample size (100) is big enough to use Z-test for the hypothesis (color compositions of candies)

Null hypothesis: "Composition content of red candies = 14%", etc. (each color has 1 corresponding hypothesis)

=> We need to calculate the Z-statistic; which we will be able to calculate by the following steps:-

Step 1: Copy all data to an Excel sheet

Step 2: Calculate mean of composition %age for each color

Step 3: Calculate standard deviation of composition %age for each color

Step 4: Significance testing levels: 99% => Two-tailed alpha = 0.005 and 0.995

Step 5: Z-critical value(s) --> -2.57 and 2.57

The Confidence interval for composition of each color = [ mean - 2.57*(std. dev.), mean + 2.57*(std. dev.) ]

If the composition corresponding to each color (given in the question) lies between the confidence interval calculated for that color, then the null hypothesis for that color is accepted. Otherwise, it should be rejected.

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