5. A consumer protection agency is testing a sample of cans of tomato soup from

Question

5. A consumer protection agency is testing a sample of cans of tomato soup from a company. If they find evidence that the average level of the chemical bisphenol A (BPA) in tomato soup from this company is greater than 100 ppb (parts per billion), they will recall all the soup and sue the company.

(a) State the null and alternative hypotheses (in symbols).

(b)Using the context of the problem, what would a Type I Error be in this situation?

(c)Using the context of the problem, what would a Type II Error be in this situation?

(d) Suppose a sample of 50 tomato cans was taken, and the sample mean was found to be 106 ppb. A randomization distribution is to be used to find the p-value. Here, the p-value is the proportion of sample means in the randomization distribution that are ________________________ [less than/greater than] or equal to __________ , under the assumption that __________ = __________ .

Explanation / Answer

Question a)

Ho: µ = 100

Ha: µ > 100

Question b)

Type I Error: We reject Ho, when Ho is true

Type I Error will occur when by mistake we conclude that the average level of the chemical bisphenol A (BPA) in tomato soup from this company is greater than 100 ppb but actually it is equal to 100 ppb.

Question c)

Type II Error: We accept Ho, when Ho is false.

Type II Error will occur when by mistake we conclude that the average level of the chemical bisphenol A (BPA) in tomato soup from this company is equal to 100 ppb but actually it is greater than 100 ppb.

Question d)

Here the p-value is the proportion of sample means in the randomization distribution that are greater than or equal to test statistics under the assumption that µ = 100.

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