Conclusion

Conclusion

Proportion Tests (each one compares the true proportion of two different colors in a bag)

In our first test, we wanted to determine whether the true proportion of blue M&Ms per bag was greater than the true proportion of orange M&Ms per bag. Using a two-proportion z-test, we received a p-value of 0.534. Since the p-value was greater than alpha, we failed to reject the null hypothesis at the 0.05 level of significance. Therefore, we do not have sufficient evidence to conclude that the true proportion of blue M&Ms is significantly greater than the true proportion of orange M&Ms per bag.

Our second test was to determine whether the true proportion of red M&Ms per bag was less than the true proportion of blue M&Ms per bag. We ran a two-proportion z-test and received a p-value of 0.000. Since the p-value is less than alpha, we rejected the null hypothesis at all levels of significance. Therefore, we do have sufficient evidence to conclude that the true proportion of red M&Ms is significantly less than the true proportion of blue M&Ms per bag.

In our third test, we wanted to determine whether the true proportion of green M&Ms per bag was different than the true proportion of brown M&Ms per bag. Using a two-proportion z-test, we received a p-value of 0.000. Since the p-value was less than alpha, we rejected the null hypothesis at all levels of significance. Therefore, we do have sufficient evidence to conclude that the true proportion of green M&Ms is significantly different than the true proportion of brown M&Ms per bag.

Chi-Square Test

Chi-Square Test comparing the expected proportions of each color per bag to the actual proportions

For our final test, we ran a chi-square test to determine if the proportions from our study were consistent with the proportions given by the M&M company. Since all of our expected values were greater than 5, we were able to make inferences on our results. After receiving a p-value of 0.000, we rejected the null hypothesis at all levels of significance. Therefore, we have sufficient evidence to conclude that at least one of the proportions significantly differs from the proportions stated by the M&M company.

Interesting Facts

In 1998 the M & Ms characters became self-professed spokes candies of the new Millennium since the Roman numerals MM means 2000.
In 2001 M & Ms launched a global call for a new color to add to the M & M mix. Citizens of over 200 countries took part in the survey, which was conducted by ballot, phone, website, mail, and even on site at kiosks. The result wasn't quite unanimous, but purple edged out aqua by four percentage points to become a temporary M & M color.