A sample of 453 boxes of cereal from New York weighed 1203 o

A sample of 453 boxes of cereal from New York weighed 12.03 ounces on average. A sample of 5 boxes of the same cereal from California weighed 11.59 ounces on average. Ralph Nader wants us to determine if the consumers in California are being cheated.

a) Propose a model for these measurements and a null and alternative hypothesis for testing if there is a significant difference between the average weights of the boxes.

b) Assume that the standard deviation of the cereal box weights is the same in both states, and use the sample standard deviations S 2 x = 0.26547 and S 2 y = 0.9673 to estimate the standard deviation of the samples. (The Xi’s are the weights of the New York’s boxes and the Yi’s are the weights of the California boxes.)

c) Calculate the appropriate test statistic for this test. What is your conclusion about the cereal boxes?

Solution

a)
Null Hypothesis : Mean(New York) = Mean(California)
Alternate Hypothesis : Mean(New York) != Mean(California)

b)
Sample SD^2x = 0.26547 / 453 = 0.00058
Sample SD^2y = 0.9673 / 5   = 0.19346

c)
z = ( 12.03 - 11.59)/ sqrt(0.00058+0.19346)
= 0.9988
  
This is a two test test,
Therefore,
P-value is = 2 * (1-0.8413) = 0.3174 Answer

Since , P > 0.05
Failed to reject null hypothesis.

There is insufficient evidence to tell about whether the consumers in California are being cheated or not.