In preparation for upcoming wage negotiations with the union, the managers for the Bevel Hardware Company want to establish the time required to assemble a kitchen cabinet. A first line supervisor believes that the job should take 40 minutes on average to complete. A random sample of 120 cabinets has an average assembly time of 42 minutes with a standard deviation of 8 minutes. Is there overwhelming evidence to contradict the first line supervisors belief at a 0.05 significance level

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true mean for the assembly time is significantly different from 40 minutes.

Step-by-step explanation:

Information provided

[tex]\bar X=42[/tex] represent the sample mean for the assembly time

[tex]s=8[/tex] represent the sample deviation

[tex]n=120[/tex] sample size

[tex]\mu_o =40[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis

We want to conduct a hypothesis in order to see if the true mean is equal to 40 minutes or not, the system of hypothesis would be:

Null hypothesis:[tex]\mu =40[/tex]

Alternative hypothesis:[tex]\mu \neq 40[/tex]

The statistic for this case is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)

Replacing the info given we got:

[tex]t=\frac{42-40}{\frac{8}{\sqrt{120}}}=2.739[/tex]

The p value for this case would be given by:

[tex]p_v =2*P(z>2.739)=0.0616[/tex]

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true mean for the assembly time is significantly different from 40 minutes.