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Answer:
The P-value you would use to test the claim that the population mean of pencils produced in that factory have a mean length equal to 18.0 cm is 0.00736.
Step-by-step explanation:
We are given that a quality control specialist at a pencil manufacturer pulls a random sample of 45 pencils from the assembly line.
The pencils have a mean length of 17.9 cm. Given that the population standard deviation is 0.25 cm.
Let = <u><em>population mean length of pencils produced in that factory.</em></u>
So, Null Hypothesis, :
= 18.0 cm {means that the population mean of pencils produced in that factory have a mean length equal to 18.0 cm}
Alternate Hypothesis, :
18.0 cm {means that the population mean of pencils produced in that factory have a mean length different from 18.0 cm}
The test statistics that will be used here is <u>One-sample z-test</u> statistics because we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean length of pencils = 17.9 cm
= population standard deviation = 0.25 cm
n = sample of pencils = 45
So, <u><em>the test statistics</em></u> =
= -2.68
The value of z-test statistics is -2.68.
<u>Now, the P-value of the test statistics is given by;</u>
P-value = P(Z < -2.68) = 1 - P(Z 2.68)
= 1- 0.99632 = 0.00368
For the two-tailed test, the P-value is calculated as = 2 0.00368 = 0.00736.