Question

Unlike most packaged food products, alcohol beverage container labels are not required to show calorie or nutrient content. 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 192 and the sample standard deviation was 86. Does this data suggest that the true average estimated calorie content in the population sampled exceeds the actual content? Test the appropriate hypotheses at significance level 0.001.

Answer 1

Answer with explanation:

Let $\mu$ be the average estimated calorie content in the population.

As per given , we have

$H_0: \mu\leq153\\\\ H_a: \mu>153$ , since the alternative hypothesis is right -tailed , so the test is a right tailed test.

Sample size : n= 58

Sample mean : $\overline{x}=192$

sample standard deviation : s= 86

Population standard deviation is unknown , so we use t-test.

Test statistic: $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

$=\dfrac{192-153}{\dfrac{86}{\sqrt{58}}}\approx3.45$

Critical value at significance level 0.001 and degree of freedom 57 (∵ df=n-1 )  :

$t_{(0.001,\ 57)}=3.239$

Decision : Test statistic value is greater than the critical value at significance level 0.001, so we reject the null hypothesis .

Conclusion : We have sufficient evidence to support the claim that the true average estimated calorie content in the population sampled exceeds the actual content.