Respuesta :
Answer:
There is insufficient statistical evidence to prove that the companies stated color distribution is not correct therefore, the overall proportions of the colors are correctly stated as above
Step-by-step explanation:
We have that
H₀: 0.24 blue, 0.13 brown, 0.20 green, 0.16 orange, 0.13 red and 0.14 yellow
The Data given are as follows;
Hₐ: The stated distribution of M&M is incorrect
Blue Brown Green Orange Red Yellow Total
Observed: 105 72 89 84 70 80 500
Expected: 120 65 100 80 65 70
We have;
[tex]\chi ^{2}=\dfrac{\left (105-120 \right )^{2}}{120}+ \dfrac{\left (72-65\right )^{2}}{65} + \dfrac{\left (89-100\right )^{2}}{100} + \dfrac{\left (84-80\right )^{2}}{80} + \dfrac{\left (70-65\right )^{2}}{65} + \dfrac{\left (80-70\right )^{2}}{70} = 5.85[/tex]
At 6 - 1 = 5 degrees of freedom we find the p-value from the chi squared table as follows
P(0.05) at 5% degrees of freedom =11.070 hence our P-value is larger than 0.05 and we fail to reject the null hypothesis, hence there is insufficient statistical evidence to prove that the companies stated color distribution is not correct.
