Question

# Use the distribution below to test that Plain M&Ms follow the stated distribution. Discuss your choice...

Use the distribution below to test that Plain M&Ms follow the stated distribution. Discuss your choice of ?. Would a different ? have changed your conclusion?
M&M states the following distribution for Plain M&Ms:
Red = 13%, Orange = 20%, Yellow = 13%, Green = 20%, Blue = 20%, Brown = 14%

Total amount of Plain M&Ms: 678

Red=69 Orange=216 Yellow=75 Green=61 Blue=187 Brown=70

We would be using the chi square goodness of fit test here to test the claim whether the distribution follows the stated distribution.

The expected frequencies for each colour is computed here as:
= Proportion of that colour expected * Total Sample size

Ei = pi*678

The computations are thus made here as:

 Colour Observed Freq Expected Freq (O_i - E_i)^2/E_i Red 69 88.14 4.1563 Orange 216 135.6 47.6708 Yellow 75 88.14 1.9589 Green 61 135.6 41.0410 Blue 187 135.6 19.4835 Brown 70 94.92 6.5424 678 678 120.8530

The chi square test statistic now is computed as shown in the last column of the above table as:

For n - 1 = 5 degrees of freedom, the p-value here is obtained from the chi square distribution tables as:

As the p-value here is approx. negligible, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the given observed frequencies are not in line with the stated distribution.

#### Earn Coins

Coins can be redeemed for fabulous gifts.