Question 952806: A chocolate company randomly fills boxes of 10 pieces of chocolate with differently typed of chocolate candies. Some have fruit filling, some caramels and others with nuts. The number of chocolates with nuts (the most popular) in each box is known to vary normally with mean of 5. A local consumer group believes that there are much less than 5 chocolates with nuts in each box. A random sample 40 boxes were chosen and fund that the mean number of chocolates with nuts is 3.3 with a standard deviation of 1.2 chocolates. Is the chocolate company putting less than 5 chocolates with nuts in each box? Use alpha=.05
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A chocolate company randomly fills boxes of 10 pieces of chocolate with differently typed of chocolate candies. Some have fruit filling, some caramels and others with nuts. The number of chocolates with nuts (the most popular) in each box is known to vary normally with mean of 5. A local consumer group believes that there are much less than 5 chocolates with nuts in each box. A random sample 40 boxes were chosen and fund that the mean number of chocolates with nuts is 3.3 with a standard deviation of 1.2 chocolates. Is the chocolate company putting less than 5 chocolates with nuts in each box? Use alpha=.05
-----
Ho: u >= 5
Ha: u < 5 (claim)
-----
sample mean = 3.3
----
z(3.3) = (3.3-5)/1.2 = -1.7/1.2 = -1.4167
------
p-value = P(z < -1.4167) = normalcdf(-100,-1.4167) = 0.0783
----
Conclusion:
Since the p-value is greater than 5%, fail to reject Ho.
The test results do not support the claim.
Chocolate company is not cheating on chocolates.
Cheers,
Stan H.
-----------
|
|
|
