Answer:
The claim that the current work teams can build room additions quicker than the time allotted for by the contract has strong statistical evidence.
Step-by-step explanation:
We have to test the hypothesis to prove the claim that the work team can build room additions quicker than the time allotted for by the contract.
The null hypothesis is that the real time used is equal to the contract time. The alternative hypothesis is that the real time is less thant the allotted for by the contract.
[tex]H_0: \mu=0\\\\H_1: \mu<0[/tex]
The significance level, as a storng evidence is needed, is α=0.01.
The estimated standard deviation is:
[tex]s_M=\frac{s}{\sqrt{n}}=\frac{0.2}{\sqrt{16}} =0.2/4=0.05[/tex]
As the standard deviation is estimated, we use the t-statistic with (n-1)=15 degrees of freedom.
For a significance level of 0.01, right-tailed test, the critical value of t is t=2.603.
Then, we calculate the t-value for this sample:
[tex]t=\frac{x-\mu}{s_M} =\frac{-0.32-0}{0.05}= -6.4[/tex]
As the t-statistic lies in the rejection region, the null hypothesis is rejected. The claim that the current work teams can build room additions quicker than the time allotted for by the contract has strong statistical evidence.
