Question

The owner of a construction company would like to know if his current work teams can build room additions quicker than the time allotted for by the contract. A random sample of 16 room additions completed recently revealed an average completion time of 0.32 days (with s = 0.2 days) faster than contracted. Is this strong evidence that the teams can complete room additions in less than the contract times? The appropria

Answer 1

The claim that the current work teams can build room additions quicker than the time allotted for by the contract has strong statistical evidence.

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.

`H_0: \mu=0\\\\H_1: \mu<0`

The significance level, as a storng evidence is needed, is α=0.01.

The estimated standard deviation is:

`s_M=(s)/(√(n))=(0.2)/(√(16)) =0.2/4=0.05`

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:

`t=(x-\mu)/(s_M) =(-0.32-0)/(0.05)= -6.4`

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.