15. M&M's plain chocolate candies come in six different colors: dark brown, yellow, red, orange, green, and blue. According to the manufacturer (Mars, Inc.), the color ration in each large production batch is 30% brown, 20% yellow, 20% red, 10% orange, 10% green, and 10% blue. To test this claim, a professor at Carleton College (Minnesota) had students count the colors of M&M's found in the "fun sized" bags of the candy (Teaching Statistics, Spring 1993). The results for 370 M&M's are displayed in the table below. Brown Yellow Red Orange Green Blue Total 84 79 75 49 36 47 370 Source: Johnson, R.W. "Testing color proportions of M&M's" Teaching Statistics. Vol 15, No. 1, Spring 1993, p.2 (Table l) a) Assuming the manufacturer's stated percentages are accurate, calculate the expected numbers falling into the six categories h) Calculate the value of x2 for testing the manufacturer's claim. c) Conduct a test to determine weather the true percentages of the colors produced differ from the manufacturer's stated percentages. Use a a = .05 16. For over 20 years, movie critic Gene Siskel (formerly of the Chicago Tribune, now deceased) and Roger Ebert (Chicago Sun-Times) rated the latest film releases on national television, first on PBS with Sneak Previews, then in syndication with At the Movies. University of Florida statisticians examined data on 160 movie reviews by Siskel and Ebert during the period 1995-1996 (Chance, Spring 1997). Each critic's review was rated pro (\"thumbs up ") or con ("thumbs down"), or mixed. Consequently, each movie has a Siskel rating (pro, con, or mixed) and an Ebert rating (pro, con, or mixed). Count Expected count Count Expected count Count Expected count Count Expected count a) Verify that the expected cell counts in the table are accurate b) Conduct a test hypothesis to determine whether the movie reviews of the two critics are independent. Use a a = .01