Step 1 :For this study, we should use a one-sample t-test.
Step 2 :The null and alternative hypotheses would be: \(H_{0}\): The average assembly time is 11 minutes. \(H_{1}\): The average assembly time is greater than 11 minutes.
Step 3 :Calculate the test statistic: The test statistic is approximately \(\boxed{0.880}\).
Step 4 :Calculate the p-value: The p-value is approximately \(\boxed{0.197}\).
Step 5 :Compare the p-value to the significance level: The p-value is greater than \(\alpha\).
Step 6 :Based on this, we should fail to reject the null hypothesis.
Step 7 :Thus, the final conclusion is that the data suggest that the population mean amount of time to assemble the Meat Man barbecue is not significantly higher than 11 at \(\alpha=0.05\), so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is higher than 11.