According to the M&M’s website, the distribution of the
colors of Milk Chocolate M&M’s should be 24% blue, 14% brown,
16% green, 20% orange, 13% red, and 14% yellow. In fun-size
packs distributed on the first day of a class, the total number of
M&M’s was 992. Out of that number, the total number of
blue M&M’s was 225.
Find the sample proportion of milk chocolate M&M’s that are
blue.
Construct a 95% confidence interval for the proportion of blue
M&M’s in the milk chocolate variety. Show the calculation
of the margin of error. Show the confidence interval that you
obtain.
Do your results agree with the website’s claim, i.e. does your
confidence interval contain the proportion stated by the M&M
company of 24% blue?
Carry out a hypothesis test to
determine whether the proportion of blue M&M’s is different
from the value stated on the website. Show the hypotheses,
the test statistic, and the p-value, with all supporting
work. State whether or not the null is rejected. State
a final conclusion, in context. Use a level of significance
of 0.05.