A simple random sample of 12 different cereals is​ obtained, and the sugar content​ (in grams of sugar per gram of​ cereal) is measured for each cereal selected. Those amounts have a mean of 0.289 gram and a standard deviation of  0.167 gram. Use a 0.05 significance level to test the claim of a cereal lobbyist that the mean for all cereals is less than 0.33 gram. Formulate the null and alternative hypotheses. Choose the correct answer below. Find the test statistic. Find the​ P-value. State the conclusion.

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