The color distribution of plain M&M's varies by the factory in which they were made. The Hackettstown, New Jersey plant uses the following color distribution for plain M&M's: 12.5% red, 25% orange, 12.5% yellow, 12.5% green, 25% blue, and 12.5% brown. Each piece of candy in a random sample of 100 plain M&M's from the Hackettstown factory was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the Hackettstown factory color distribution is correct. Describe method used for calculating answer.
Red: 9
Orange: 27
Yellow: 11
Green: 14
Blue: 22
Brown: 17
- Identify the appropriate hypothesis test and explain the reasons why it is appropriate for analyzing this data.
- Determine the test statistic. (Round your answer to two decimal places)
- Compare p-value and significance level α. What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?