Question

A popular brand of raisin bran cereal boasts that each box contains 2 cups of raisins. Suppose 36 cereal boxes are randomly sampled with a sample mean of 1.9 cups of raisins in each box with a standard deviation of 0.23 cups. Is the claimed amount within the 95% confidence interval? What can you conclude about the claim?

Answer 1

Let X denotes the number of cup of raisins in each box of cereal boasts. Given that the sample mean number of cups in a sample of 36 cereal boxes is 1.9 and the sample standard deviation is 0.23. The 95% confidence interval for mean when population standard deviation is unknown is .

Now substitute the respective values in the confidence interval.

The 95% confidence interval for the population mean number of cups of raisins is (1.822, 1.978). It is the range in which the population mean will lie at 95% confidence. The claim that each box contains 2 cups of raisins is not valid as the 95% confidence interval does not contain the value 2. So it can concluded that the claim has no evidence and it is reasonable to say that the mean number of raisins cups would be less than 2.