Determine the appropriate test to use for the study:
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The commercial for the new Meat Man Barbecue claims that it takes 11 minutes for assembly. A consumer advocate thinks that the assembly time is higher than 11 minutes. The advocate surveyed 14 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 11.8 minutes. The standard deviation for this survey group was 3.4 minutes. What can be concluded at the the $\alpha=0.05$ level of significance level of significance?
a. For this study, we should use Select an answer
b. The null and alternative hypotheses would be:
\[
\begin{array}{l}
H_{0}: ? \vee \text { Select an answer } \vee \\
H_{1}: ? \vee \text { Select an answer } \vee
\end{array}
\]
c. The test statistic $? \vee=\square$ (please show your answer to 3 decimal places.)
d. The $p$-value $=\square$ (Please show your answer to 4 decimal places.)
e. The $p$-value is $? \vee \alpha$
$f$. Based on this, we should Select an answer $\vee$ the null hypothesis.
g. Thus, the finat conclusion is that ...
The data suggest the populaton mean is significantly higher than 11 at $\alpha=0.05$, so there is statistically significant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is higher than 11.
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.
The data suggest the population mean 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 equal to 11.
Hint: Heip
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Answer
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.
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.
