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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.
<u><em>Let </em></u><u><em> = average time to assemble an electronic component.</em></u>
SO, Null Hypothesis, :
= 14 minutes {means that the average time to assemble an electronic component is equal to 14 minutes}
Alternate Hypothesis, :
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 <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample average time for completion = 11.6 minutes
= population standard deviation = 3.4 minutes
n = sample of components = 14
So, <u><em>test statistics</em></u> =
= -2.64
<u>Now, P-value of the hypothesis test is given by the following formula;</u>
P-value = P(Z < -2.64) = 1 - P(Z 2.64)
= 1 - 0.99585 = 0.0042
Hence, the p-value for the hypothesis test is 0.0042.