A food scientist claims that the mean sodium content in a brand of canned soup is at most 500500 mg\text{mg} per serving. A random sample of 3636 cans yields a sample mean of 560560 mg\text{mg} and a sample standard deviation of 120120 mg\text{mg}. At α=0.01\alpha=0.01, is there sufficient evidence to reject the scientist’s claim?

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Performing Hypothesis Tests: Means

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Problem 28Multiple Choice

A food scientist claims that the mean sodium content in a brand of canned soup is at most $500$ $mg$ per serving. A random sample of $36$ cans yields a sample mean of $560$ $mg$ and a sample standard deviation of $120$ $mg$ . At $alpha equals 0.01$ , is there sufficient evidence to reject the scientist’s claim?

Yes, there is sufficient evidence to conclude that the mean sodium content exceeds $500$ $mg$ per serving.

No, there is insufficient evidence to conclude that the mean sodium content exceeds $500$ $mg$ per serving.

The test is inconclusive.

More data is needed.

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