Answer:
We conclude that the true average estimated calorie content in the population sampled exceeds the actual content.
Step-by-step explanation:
We are given that an article 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.
Let = <u><em>true average estimated calorie content in the population sampled.</em></u>
So, Null Hypothesis, :
153 calories {means that the true average estimated calorie content in the population sampled does not exceeds the actual content}
Alternate Hypothesis, :
> 153 calories {means that the true average estimated calorie content in the population sampled exceeds the actual content}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean estimated calorie level = 193 calories
s = sample standard deviation = 88
n = sample of individuals = 58
So, <u><em>the test statistics</em></u> = ~
= 3.462
The value of t test statistics is 3.462.
Since, in the question we are not given the level of significance so we assume it to be 5%. <u>Now, at 0.05 significance level the t table gives critical value of 1.6725 at 57 degree of freedom for right-tailed test.</u>
Since our test statistic is more than the critical value of t as 3.462 > 1.6725, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that the true average estimated calorie content in the population sampled exceeds the actual content.