Question

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. How would you calculate the p-value for the hypothesis test

Answer 1

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 $\mu$ = average time to assemble an electronic component.

SO, Null Hypothesis, $H_0$ : $\mu$ = 14 minutes  {means that the average time to assemble an electronic component is equal to 14 minutes}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ 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.  = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$  ~ N(0,1)

where, $\bar X$ = sample average time for completion = 11.6 minutes

             $\sigma$ = population standard deviation = 3.4 minutes

             n = sample of components = 14

So, test statistics  =  $\frac{11.6-14}{\frac{3.4}{\sqrt{14} } }$  

                               =  -2.64

Now, P-value of the hypothesis test is given by the following formula;

         P-value = P(Z < -2.64) = 1 - P(Z $\leq$ 2.64)

                                              = 1 - 0.99585 = 0.0042

Hence, the p-value for the hypothesis test is 0.0042.