Question

The commercial for the new Meat Man Barbecue claims that it takes 12 minutes for assembly. A consumer advocate thinks that the assembly time is lower than 12 minutes. The advocate surveyed 15 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 10.1 minutes. The standard deviation for this survey group was 2.2 minutes. What can be concluded at the the αα = 0.01 level of significance level of significance?

For this study, we should use Select an answer t-test for a population mean z-test for a population proportion

The null and alternative hypotheses would be:

H0:H0:  ? p μ  Select an answer > ≠ < =       

H1:H1:  ? μ p  Select an answer > = < ≠    

The test statistic ? t z  =  (please show your answer to 3 decimal places.)

The p-value =  (Please show your answer to 4 decimal places.)

The p-value is ? ≤ >  αα

Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.

Thus, the final conclusion is that ...

The data suggest the population mean is not significantly lower than 12 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is equal to 12.

The data suggest the populaton mean is significantly lower than 12 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 12.

The data suggest that the population mean amount of time to assemble the Meat Man barbecue is not significantly lower than 12 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 12.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 12
Alternative Hypothesis, Ha: μ < 12

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (10.1 - 12)/(2.2/sqrt(15))
t = -3.345

P-value Approach
P-value = 0.0024
As P-value < 0.01, reject the null hypothesis.

The data suggest the populaton mean is significantly lower than 12 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 12.