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

Given that 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.

H0: µ = 12 against H1: µ < 12

n =4

std error = [tex]\frac{0.5}{\sqrt{4} } =0.25[/tex]

Mean difference [tex]= 11.25 -12 = -0.75[/tex]

Test statistic t = mean diff/std error = -3

p value=0.00135 <0.05 our significance level

So reject H0

There is evidence to prove that mean is less than 12 kg.