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 upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.25. round your final answer to five decimal places (e. g. 98.76543).

Question

Cedric Hayden

Mathematics

22 July, 04:48

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 upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.25. round your final answer to five decimal places (e. g. 98.76543).

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Sawyer Ingram · Answer 1

We solve this by using the z statistic, the formula for z score is:

z = (x - u) / s

where x is the sample value = 11.25, u is the mean = 12, and s is the standard deviation = 0.5

z = (11.25 - 12) / 0.5

z = - 1.5

From the standard probability tables, the p value is:

P = 0.06680