Question

The commercial for the new Meat Man Barbecue claims that it takes 10 minutes for assembly. A consumer advocate thinks that the claim is false. The advocate surveyed 50 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 11.2 minutes. The standard deviation for this survey group was 3.1 minutes. What can be concluded at the 0.05 level of significance?H0: mu.gif= 10Ha: mu.gif [ Select ] [">", "<", "Not Equal to"] 10Test statistic: [ Select ] ["Chi-square", "F", "Z", "t"] p-Value = [ Select ] ["0.105", "0.009", "0.091", "0.025"] . Round your answer to three decimal places. [ Select ] ["Reject the null hypothesis", "Fail to reject the null hypothesis"] Conclusion: There is [ Select ] ["sufficient", "insufficient"] evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is not equal to 10 minutes.

Answer 1

Answer:

There is enough evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is not equal to 10 minutes (P-value=0.009).

Step-by-step explanation:

We have to perform an hypothesis test on the mean.

The null and alternative hypothesis are:

$H_0: \mu=10\\\\H_1: \mu \neq 10$

The significance level is $\alpha=0.05$.

The test statistic t can be calculated as:

$t=\frac{M-\mu}{s/\sqrt{N} } =\frac{11.2-10}{3.1/\sqrt{50} }=2.737$

The degrees of freedom are:

$df=N-1=50-1=49$

The P-value (two-tailed test) for t=2.737 and df=49 is P=0.00862.

This P-value (0.009) is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.

There is enough evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is not equal to 10 minutes.