Question

The commercial for the new Meat Man Barbecue claims that it takes 14 minutes for assembly. A consumer advocate thinks that the assembly time is different than 14 minutes. The advocate surveyed 11 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 12.6 minutes. The standard deviation for this survey group was 2.6 minutes. a) What is the Null and alternative hypotheses. b) What can be concluded at the the a = 0.05 level of significance level of signifi- cance? c) In words what is your final conclusion.

Answer 1

( a )

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested: Ho: u = 14 Haut 14

( b )

Rejection Region Based on the information provided the significance level is a = 0.05, and the critical value for a two- tailed test is te = 2.228 The rejection region for this two-talled test is R = {t: 't > 2.228} Test Statistics The t-statistic is computed as follows: X-30 106-14 = 1.786 26/11 Decision about the nul bycothesis Since it is observed that t = 1.786 <te = 2.228. It is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p = 0.1044, and since p=0.1044 > 0.05, it is concluded that the null hypothesis is not rejected

( c )

Conclusion :

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is enough evidence to claim that

it takes 14 minutes for assembly at the 0.05 significance level.