Respuesta :
Answer:
Null hypothesis is rejected. There is no or little evidence to support the claim made by Mars.In
Step-by-step explanation:
Solution:-
- A claim is made by Mars.In that the M&M candies in a packet are distributed by color percentage given below.
- A random sample of N = 460 M&M's was taken and the frequencies of different colors were observed as given below.
- We are to test a claim made by the Mars.In regarding the color distribution of M&Ms at significance level α = 0.05.
- Compute the expected frequency of distribution for color as per Mars.In claim. Use the following formula for expected outcome:
Expected = N*pi
Where, pi : The percentages for each color.
- The table for expected and observed frequencies for each color is tabulated below.
Colors Percentage Expected Observed
Brown 20% 460*0.2 = 92 90
Yellow 20% 460*0.2 = 92 94
Red 30% 460*0.3 = 138 99
Orange 10% 460*0.1 = 46 64
Green 10% 460*0.1 = 46 51
Blue 10% 460*0.1 = 46 62
- To test the claim for color distribution of M&Ms using X^2 - test. We will state the Null and Alternate hypothesis as follows:
Null Hypothesis: The distribution is colors is as its claimed by the company
Alternate Hypothesis: The distribution is colors is not its claimed by the company
- We will first determine the X^2 statistics value using the following relation:
[tex]X^2-test = Sum [ \frac{(Oi- Ei)^2}{Ei} ]\\\\X^2-test = \frac{(90- 92)^2}{92} + \frac{(94- 92)^2}{92} + \frac{(99- 138)^2}{138} + \frac{(64- 46)^2}{46} + \frac{(51- 46)^2}{46} + \frac{(62- 46)^2}{46} \\\\X^2-test = \frac{4}{92} + \frac{4}{92} + \frac{1521}{138} + \frac{324}{46} + \frac{25}{46} + \frac{256}{46} \\\\X^2-test = 0.04347 + 0.04347 + 11.0217 + 7.04348 + 0.54348 + 5.56522\\\\X^2-test = 24.2608[/tex]
- The rejection region is defined by the significance level ( α ) = 0.05 and degree of freedom. The bound ( critical value ), X^2-critical is determined using the look-up table:
degree of freedom = number of observation category - 1 = 6 - 1 = 5
P ( X < X^2 - critical ) = 0.025
X^2 - critical = 12.8
- All the test values of X^2 > X^2-critical lie in the rejection region.
24.2608 > 12.8
X^-test > X^2-critical
Hence, Null hypothesis is rejected.
Conclusion: As per Chi-square test the claim made by the Mars.In has little or no evidence to be true; hence, the color distribution of M&M is not what is claimed.
