Unlike most packaged food products, alcohol beverage container labels are not required to show calorie or nutrient content. An a

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Unlike most packaged food products, alcohol beverage container labels are not required to show calorie or nutrient content. An a

rticle reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories. The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88. Does this data suggest that the true average estimated calorie content in the population sampled exceeds the actual content

Mathematics

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AnnZ [12.3K] · Answer 1 · 2026-04-03T03:26:36+03:00

We determine that the true average calorie content as estimated in the sampled population surpasses the actual calorie content. Step-by-step explanation: An article discussed a pilot study where each of the 58 participants was asked to estimate the calorie count of a 12 oz beer known to have 153 calories. The observed sample mean of calorie estimation was 193, with a sample standard deviation of 88. Let $\mu$ = true average estimated calorie level within the sampled population. Thus, Null Hypothesis, : $\mu$ 153 calories {indicating that the true average estimated calorie content does not exceed the actual amount}. Alternative Hypothesis, $H_A$ : $\mu$ > 153 calories {indicating the true average estimation exceeds the actual}. The appropriate test statistic would be a one-sample t-test statistic, as we lack knowledge of the population standard deviation; Test Statistic = ~t = $t_n_-_1$

where, sample mean estimated calorie level = 193 calories, s = sample standard deviation = 88, and n = sample size = 58. Therefore, the test statistic = ~t = 3.462. The t-table indicates a critical value of 1.6725 for 57 degrees of freedom at a 0.05 significance level. Since our test statistic of 3.462 > 1.6725, we have sufficient evidence to reject the null hypothesis; thus, affirming that the true average estimated calorie content in the sampled population exceeds the real content.