A textile fiber manufacturer is investigating a new drapery yarn, which the comp

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: = 12 against H1: < 12, using a random sample of four specimens.

(b) Find for the case where the true mean elongation is 11.25 kilograms.

(c) Find for the case where the true mean is 11.5 kilograms.

find the boundary of the critical region if the type I error probability is

(d) = 0.01 and n = 4

(e) = 0.05 and n = 4

(f) = 0.01 and n = 16

(g) = 0.05 and n = 16

calculate the probability of a type II error if the true mean elongation is 11.5 kilograms and

(h) = 0.05 and n = 4

(i) = 0.05 and n = 16

(j) Compare the values of calculated in the previous parts. What conclusion can you draw?

calculate the P-value if the observed statistic is

(k) xbar = 11.25

(l) xbar = 11.0

(m) xbar = 11.75

Explanation / Answer

H0: µ = 12

H1: µ < 12

Standard deviation = 0.5

Part a)

We know that,

z = (x bar – Mean) / ( SD / sqrt(n))

= (11.5 – 12)/(0.5/sqrt(4))

= -2

P (z<-2) = 0.0228 ~ 0.02

Answer: 0.02

Part b)

Here our critical z is -2

X bar = 11.5

P ( x bar > 11.5)

z = (11.5 – 11.25)/(0.5/sqrt(4))

   = 1

z = 1

P ( z > 1 ) = 1 – P ( z < 1 )

                 = 1 – 0.1587

                 = 0.8413

Answer: 0.8413

Part c)

P ( x bar > 11.5)

z = (11.5 – 11.5)/(0.5/sqrt(4))

   = 0

z = 0

P ( z > 0 ) = 1 – P (z < 0)

                 = 1 – 0.5

                 = 0.5

Answer: 0.5

Part d)

a = .01 and n = 4

From normal table we get the critical value as -2.33

Answer: -2.33

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.