A manufacturer of children's vitamins claims that its vitamins are mixed so that each batch has exactly the following percentages of each color: 20%green, 30%yellow, 30%red, and20%orange. To test the claim that these percentages are incorrect, 100 bottles of vitamins weresampledand the colors of the vitamins were tallied. The results are listed in the following table. At=0.005, determine whether there issufficientevidence to conclude that the percentages stated by the vitamin manufacturer are incorrect.

Children's Vitamins Green 591

Yellow 856

Red 858

Orange 508

Calculate the expected value for the number of vitamins that are red. Round your answer to three decimal places, if necessary

Compute the value of the test statistic.Round any intermediate calculations to at least six decimal places, and round your final answer to three decimal places.

Also determine the p-value