For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
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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 
= true average estimated calorie level within the sampled population. Thus, Null Hypothesis, : 153 calories {indicating that the true average estimated calorie content does not exceed the actual amount}. Alternative Hypothesis, 
: > 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 = 
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.
