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

A hypothesis test can be conducted to test the claim made in the commercial for the new Meat Man Barbecue. The test results indicate that there is evidence to support that the population mean assembly time is not equal to 10 minutes.

Step-by-step explanation:

To test the claim made in the commercial for the new Meat Man Barbecue, a hypothesis test can be conducted. The null hypothesis, H0, states that the population mean assembly time is 10 minutes, while the alternative hypothesis, Ha, states that it is not equal to 10 minutes. The test statistic to use in this case is the t-test, as we are comparing the sample mean to a known value. The p-value for this test is 0.009, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to support that the population mean assembly time is not equal to 10 minutes.

Answer 2

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 \\eq 10`

The significance level is
`\alpha=0.05`.

The test statistic t can be calculated as:

`t=(M-\mu)/(s/√(N) ) =(11.2-10)/(3.1/√(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.