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 Ho : u = 12 against Hi : j < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is ñ = 11.5. Round your final answer to five decimal places (e.g. 98.76543). 0.02883

Answer 1

1)

As the standard deviation is known here we can use standard normal z table to estimate the answer

Test statistics z = (sample mean - claimed mean )/(s.d/√n)

Z = (11.5 - 12)/(0.5/√4) = -2

From z table, P(z<-2) = 0.0228

So

P-value is = 0.0228

2)

As the population s.d is given

We can use z table here

Given alpha = 0.05

From z table, P(z>1.645) = 0.05

So critical value is = 1.645

Now

1.645 = (x - mean)/s.d

1.645 = (x - 175)/20

X = 207.9