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 56 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 levels 192 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 State the appropriate null and alternative hypotheses O Ho: 153 H < 153 | 0 H = 153 H: 153 O HON - 153 H: > 153 Ho: x = 153 HMS 153 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) P-value State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content Reject the null hypothesis. There is sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. O Do not reject the null hypothesis. There is not sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content Reject the null hypothesis. There is not sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content may need to use the appropriate table in the Appendix of Tables to answer this question

Answer 1

Ans c)

$H_{o}:\mu = 153$

$H_{a}:\mu > 153$

Explanation: Alternate Hypothesis (claim) calorie content in the population exceed (">")

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Sample size n = 56

Sample mean $\bar{x} = 192$

Sample standard deviation s = 86

Since sample size n > 30 we will assume sample sd $\approx$ population sd and do z-test

Test statistics:

n

$= \frac{192-153}{\frac{86}{\sqrt{56}}}$

$=3.39$

Therefore,

z = 3.39

p-value = 0.0003

Since, P-value < 0.001

B) Reject the null hypothesis. There is sufficient evidence that the true average estimated calorie content of the beer exceeds the actual content.