Respuesta :
Answer:
The p-value for the hypothesis test is 0.0042.
Step-by-step explanation:
We are given that the supervisor of a production line wants to check if the average time to assemble an electronic component is different from 14 minutes.
Assume that the population of assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion is 11.6 minutes.
Let [tex]\mu[/tex] = average time to assemble an electronic component.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 14 minutes {means that the average time to assemble an electronic component is equal to 14 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 14 minutes {means that the average time to assemble an electronic component is different from 14 minutes}
The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average time for completion = 11.6 minutes
[tex]\sigma[/tex] = population standard deviation = 3.4 minutes
n = sample of components = 14
So, test statistics = [tex]\frac{11.6-14}{\frac{3.4}{\sqrt{14} } }[/tex]
= -2.64
Now, P-value of the hypothesis test is given by the following formula;
P-value = P(Z < -2.64) = 1 - P(Z [tex]\leq[/tex] 2.64)
= 1 - 0.99585 = 0.0042
Hence, the p-value for the hypothesis test is 0.0042.
