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## A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with

Question

A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: µ = 12 against H1: µ < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is Xbar (average) = 11.25. Suppose that the distribution of the sample mean is approximately normal.

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Mathematics
1 year
2021-08-06T15:13:04+00:00
2021-08-06T15:13:04+00:00 1 Answers
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## Answers ( )

Answer:The p-value of the test is 0.0013.

Step-by-step explanation:The test statistic is:[tex]z = \frac{X – \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

12 is tested at the null hypothesis:This means that [tex]\mu = 12[/tex]

Standard deviation of 0.5 kilograms.This means that [tex]\sigma = 0.5[/tex]

Sample of n = 4 specimens. Observed statistic is Xbar (average) = 11.25.This means that [tex]n = 4, X = 11.25[/tex]

Value of the test statistic:[tex]z = \frac{X – \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{11.25 – 12}{\frac{0.5}{\sqrt{4}}}[/tex]

[tex]z = -3[/tex]

P-value:Probability of finding a sample mean belo 11.25, which is the p-value of z = -3.

Looking at the z-table, z = -3 has a p-value of 0.0013, thus the this is the p-value of the test.