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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 55 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? Test the appropriate hypotheses at significance level 0.001. State the appropriate null and alternative hypotheses. 153 Ha: > 153 Ho: Ho: Ha: 153 Ho: #= 153 153 H₂: HS 153 Ho: #= 153 H₂: # < 153 z = 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. 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 not sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. 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. Do not reject the null hypothesis. There is sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. You may need to use the appropriate table in the Appendix of Tables to answer this 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 55 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? Test the appropriate hypotheses at significance level 0.001. State the appropriate null and alternative hypotheses. 153 Ha: > 153 Ho: Ho: Ha: 153 Ho: #= 153 153 H₂: HS 153 Ho: #= 153 H₂: # < 153 z = 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. 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 not sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. 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. Do not reject the null hypothesis. There is sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. You may need to use the appropriate table in the Appendix of Tables to answer this question.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Hypothesis Testing for Caloric Content in Beer 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 55 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? Test the appropriate hypotheses at a significance level of 0.001. #### 1. State the Null and Alternative Hypotheses: - \( H_0: \mu = 153 \) - \( H_a: \mu > 153 \) - \( H_0: \mu = 153 \) - \( H_a: \mu \neq 153 \) - \( H_0: \mu = 153 \) - \( H_a: \mu < 153 \) - \( H_0: \mu = 153 \) - \( H_a: \mu \leq 153 \) #### 2. Calculate the Test Statistic and Determine the P-value: - Calculate \( z \): - Calculate P-value: *(Round your test statistic to two decimal places and your P-value to four decimal places.)* #### 3. State the Conclusion in the Problem Context: - 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 not sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. - 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. - Do not reject the null hypothesis. There is sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. You may need to use the appropriate table in the Appendix of Tables to answer this question. --- This exercise guides you through hypothesis testing, helping you draw conclusions about the estimated versus actual calorie content of beer based on a sample.
Transcribed Image Text:### Hypothesis Testing for Caloric Content in Beer 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 55 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? Test the appropriate hypotheses at a significance level of 0.001. #### 1. State the Null and Alternative Hypotheses: - \( H_0: \mu = 153 \) - \( H_a: \mu > 153 \) - \( H_0: \mu = 153 \) - \( H_a: \mu \neq 153 \) - \( H_0: \mu = 153 \) - \( H_a: \mu < 153 \) - \( H_0: \mu = 153 \) - \( H_a: \mu \leq 153 \) #### 2. Calculate the Test Statistic and Determine the P-value: - Calculate \( z \): - Calculate P-value: *(Round your test statistic to two decimal places and your P-value to four decimal places.)* #### 3. State the Conclusion in the Problem Context: - 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 not sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. - 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. - Do not reject the null hypothesis. There is sufficient evidence that the true average estimated calorie content of this beer exceeds the actual content. You may need to use the appropriate table in the Appendix of Tables to answer this question. --- This exercise guides you through hypothesis testing, helping you draw conclusions about the estimated versus actual calorie content of beer based on a sample.
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