In Data 4.5 on page 228 we describe a situation in which a restaurant chain will test for arsenic levels in a sample of chickens from a supplier. If there is evidence that the average level of arsenic is over 80 ppb, the chain will permanently cancel its relationship with the supplier. The null and alternative hypotheses are H₀: μ = 80 vs H_a: μ > 80.

(a) What would it mean for analysts at the restaurant chain to make a Type I error in the context of this situation?

(b) What would it mean to make a Type II error in this situation?

(c) Does the word ‘‘error” mean that the person doing the test did something wrong (perhaps by sampling in a way that biased the results, making a mistake in data entry, or an arithmetic error)? Explain.  

Data 4.5 on page 228

Arsenic-based additives in chicken feed have been banned by the European Union but are mixed in the diet of about 70% of the 9 billion broiler chickens produced annually in the US.7 Many restaurant and supermarket chains are working to reduce the amount of arsenic in the chicken they sell. To accomplish this, one chain plans to measure, for each supplier, the amount of arsenic in a random sample of chickens. The chain will cancel its relationship with a supplier if the sample provides sufficient evidence that the average amount of arsenic in chicken provided by that supplier is greater than 80 ppb (parts per billion).