A cannery claims that its sardine cans have a net weight of 8 oz., with a standard deviation of 0.1 oz. You take a simple random sample of 30 cans and encounter a sample mean of 7.85 oz. Does this provide convincing evidence to reject the claimed weight of 8 oz?
What will be an ideal response?
The sampling distribution of is normal (since n30) with mean and standard deviation given by E() = = 8, and SE() = = 0.0183, respectively.Therefore, P( < 7.8) = P(Z< -8.2) = 0. If the claim were true, such a sample would not be encountered. We have convincing evidence to reject the cannery’s claim.
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