Answer:
Calculated χ² = 13.425
χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24
The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.
Step-by-step explanation:
Color Blue Orange Green Red Yellow Brown
Frequency 30 48 55 66 70 131
Expected 40 40 40 80 80 120
H0: The bag of plain M&Ms is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown
Ha: The color distribution is not equal to the distribution stated in the null hypothesis.
Calculate chi square
χ² = (30-40)² /40 + (48-40)²/40 + (55-40)²/40 + (66-80)²/80 + (70-80)²/80 + (131-120)²/120
χ² = 2.5 + 1.6 + 5.625 + 2.45 + 1.25= 13.425
The critical region for χ² for 5 degrees of freedom with ∝= 0.05 is
χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24
The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.
