The commercial for the new Meat Man Barbecue claims that it takes 14 minutes for assembly. A consumer advocate thinks that the assembly time is different than 14 minutes. The advocate surveyed 11 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 12.9 minutes. The standard deviation for this survey group was 3.3 minutes. What can be concluded at the the a = 0.05 level of significance level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Но: ? ? H1: ? c. The test statistic ? O = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.)

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**Educational Website Transcription: Statistical Analysis of Assembly Times for the Meat Man Barbecue**

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**Scenario Analysis**

A commercial for the new Meat Man Barbecue claims that assembling the product takes 14 minutes. A consumer advocate suspects that the assembly time is different from the stated 14 minutes. To investigate, the advocate surveyed 11 randomly selected people who had purchased the Meat Man Barbecue and found their average assembly time to be 12.9 minutes, with a standard deviation of 3.3 minutes. This study explores the potential conclusion at a significance level of \( \alpha = 0.05 \).

**Hypothesis Setup**

**a. Determining the Test Type**

- A selection needs to be made on the appropriate statistical test type.

**b. Null and Alternative Hypotheses**

- Null Hypothesis (\( H_0 \)): The population mean assembly time is 14 minutes.
- Alternative Hypothesis (\( H_1 \)): The population mean assembly time is different from 14 minutes.

**Statistical Calculations**

**c. Test Statistic**

- Calculate the test statistic \( t \) and express the answer to three decimal places.

**d. P-value Calculation**

- Determine the p-value and express it to four decimal places.

**e. Comparison with Significance Level**

- Compare the p-value with the significance level \( \alpha = 0.05 \).

**f. Decision on Null Hypothesis**

- Based on the results, decide whether to "fail to reject" or "reject" the null hypothesis.

**g. Final Conclusion**

- Conclude the statistical significance as follows:

  1. The data suggests the population mean is *not significantly different* from 14 at \( \alpha = 0.05 \), indicating statistically insignificant evidence to conclude that the mean assembly time equals 14.
  
  2. The data suggests the population mean amount of time is *not significantly different* from 14 at \( \alpha = 0.05 \), indicating statistically insignificant evidence that the mean assembly time is different from 14.
  
  3. The data suggests the population mean is *significantly different* from 14 at \( \alpha = 0.05 \), indicating statistically significant evidence that the mean assembly time is different from 14.

**Hint for Decision Making**

The calculated statistics will guide whether the average assembly time indeed differs significantly from the stated time of 14 minutes.
Transcribed Image Text:**Educational Website Transcription: Statistical Analysis of Assembly Times for the Meat Man Barbecue** --- **Scenario Analysis** A commercial for the new Meat Man Barbecue claims that assembling the product takes 14 minutes. A consumer advocate suspects that the assembly time is different from the stated 14 minutes. To investigate, the advocate surveyed 11 randomly selected people who had purchased the Meat Man Barbecue and found their average assembly time to be 12.9 minutes, with a standard deviation of 3.3 minutes. This study explores the potential conclusion at a significance level of \( \alpha = 0.05 \). **Hypothesis Setup** **a. Determining the Test Type** - A selection needs to be made on the appropriate statistical test type. **b. Null and Alternative Hypotheses** - Null Hypothesis (\( H_0 \)): The population mean assembly time is 14 minutes. - Alternative Hypothesis (\( H_1 \)): The population mean assembly time is different from 14 minutes. **Statistical Calculations** **c. Test Statistic** - Calculate the test statistic \( t \) and express the answer to three decimal places. **d. P-value Calculation** - Determine the p-value and express it to four decimal places. **e. Comparison with Significance Level** - Compare the p-value with the significance level \( \alpha = 0.05 \). **f. Decision on Null Hypothesis** - Based on the results, decide whether to "fail to reject" or "reject" the null hypothesis. **g. Final Conclusion** - Conclude the statistical significance as follows: 1. The data suggests the population mean is *not significantly different* from 14 at \( \alpha = 0.05 \), indicating statistically insignificant evidence to conclude that the mean assembly time equals 14. 2. The data suggests the population mean amount of time is *not significantly different* from 14 at \( \alpha = 0.05 \), indicating statistically insignificant evidence that the mean assembly time is different from 14. 3. The data suggests the population mean is *significantly different* from 14 at \( \alpha = 0.05 \), indicating statistically significant evidence that the mean assembly time is different from 14. **Hint for Decision Making** The calculated statistics will guide whether the average assembly time indeed differs significantly from the stated time of 14 minutes.
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