Question

How strong a force (in pounds) is needed to pull apart pieces of wood 4 inches long and 1.5 inches square? The following are data from students performing a comparable laboratory exercise. Suppose that the strength of pieces of wood like these follow a Normal distribution with population standard deviation of σ = 3000 pounds.

33,200	31,870	32,550	26,540	33,280
32,300	33,050	32,030	30,510	32,720
23,090	30,940	32,700	33,650	32,390
24,060	30,150	31,290	28,710	31,880

(a) We are interested in statistical significant evidence at the

α = 0.10

level against the claim that the mean is 32,500 pounds.

What are the null and alternative hypotheses?

H₀: μ ≠ 32,500
H₁: μ = 32,500H₀: μ = 32,500
H₁: μ > 32,500    H₀: μ = 32,500
H₁: μ ≠ 32,500H₀: μ = 32,500
H₁: μ < 32,500

What is the value of the test statistic. (Round your answer to two decimal places.)
z =

What is the P-value of the test? (Round your answer to four decimal places.)
P-value =

What is your conclusion?

There is enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.    

(b) We are interested in statistical significant evidence at the

α = 0.10

level against the claim that the mean is 31,500 pounds.

What are the null and alternative hypotheses?

H₀: μ = 31,500
H₁: μ > 31,500H₀: μ = 31,500
H₁: μ ≠ 31,500    H₀: μ ≠ 31,500
H_a: μ = 31,500H₀: μ = 31,500
H₁: μ < 31,500

What is the value of the test statistic. (Round your answer to two decimal places.)
z =

What is the P-value of the test? (Round your answer to four decimal places.)
P-value =

What is your conclusion?

There is enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.    

Answer 1

Ans:

a)

H0: μ = 32,500
H1: μ ≠ 32,500

sample mean=30835.50

n=20

Test statistic:

z=(30845.5-32500)/(3000/SQRT(20))

z=-2.47

p-value(2 tailed)=2*P(z<-2.47)=0.0136

There is enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.

b)

H0: μ = 31,500
H1: μ ≠ 31,500  

sample mean=30835.50

n=20

Test statistic:

z=(30845.5-31500)/(3000/SQRT(20))

z=-0.98

p-value(2 tailed)=2*P(z<-0.98)=0.3271

*(if exact z value is considered,then p-value=0.3292)

There is not enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.