Question: You are a food inspector for the government and are tasked with investigating the company American Canned Goods for violating safe food canning and preparation laws and regulations. American Canned Goods has 135 canning locations around the United States. After randomly selecting just one canning location, you sampled 144 cans to 1) determine if the sampled cans have a higher proportion of insect parts per can compared to the population proportion of insect parts per can in the US, and 2) whether or not the cans you sampled have more protein bits (an index of insect parts). You know that the population proportion of insect parts per can in the US is .155. You measure protein bits quantitatively by counting the number of protein bits that occur in each of the 144 sampled cans. You use this index because you know that μ = 8 and σ = 2.5 protein bits in the US.

1. After collecting the sample of 144 cans, you find that the sample proportion is .203. Is your sample of cans statistically significantly filled with a higher proportion of insect parts compared to all other canned goods in the US (use α = .05, two-tailed)?
2. After collecting the sample of 144 cans, you find that sample mean = 18.33 protein bits per can. Is your sample statistically significantly associated with more protein bits per can compared to cans in the US population (use α = .05, two-tailed)?
3. In the sample of 144 cans, let’s say you obtained an x-bar of 16.5 protein bits per can. Let’s also pretend that μ is unknown. What is the least biased point estimate of μ, assuming the research design is flawless?
4. Using interval estimation, please construct 90% confidence intervals around the sample proportion of .203. Please interpret this interval. What does it mean?
5. If you want a margin of error of no more than 1 protein bits at a confidence level of 95%, how many cans would you need to collect for the sample?
6. In a sample of 144 cans, please construct an 87.3% confidence interval around the x-bar of 18.33 protein bits per can.  Please interpret this interval. What does it mean?

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