How heavy a load (pounds) is needed to pull apart pieces of wood 4 inches long a

Question

How heavy a load (pounds) is needed to pull apart pieces of wood 4 inches long and 1.5 inches square? Here are data from students doing a laboratory exercise.

We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of wood. Engineers also commonly assume that characteristics of materials vary Normally. Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 3000 pounds.

(a) Is there statistically significant evidence at the

= 0.10

level against the hypothesis that the mean is 32,500 pounds for the two-sided alternative?

What are the null and alternative hypotheses?

H0: = 32,500
Ha: > 32,500

OR

H0: = 32,500
Ha: 32,500

OR

H0: 32,500
Ha: = 32,500

OR

H0: = 32,500
Ha: < 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. OR There is not enough evidence to conclude that the wood's mean strength differs from 32,500 pounds???

(b) Is there statistically significant evidence at the

= 0.10

level against the hypothesis that the mean is 31,500 pounds for the two-sided alternative?

What are the null and alternative hypotheses?

H0: 31,500
Ha: = 31,500

OR

H0: = 31,500
Ha: 31,500

OR

H0: = 31,500
Ha: < 31,500

OR

H0: = 31,500
Ha: > 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. OR There is not enough evidence to conclude that the wood's mean strength differs from 31,500 pounds???

Please I want answers with precise calculations, check the decimals required for each question.

33,170     31,850     32,590     26,540     33,280     32,330     33,040     32,040     30,500     32,740     23,020     30,920     32,670     33,610     32,380     24,020     30,220     31,280     28,780     31,930    

Explanation / Answer

std. dev. = 3000
xbar = 30845.5
n=20

the null and alternative hypotheses are
H0: = 32,500
Ha: 32,500

test statistics, z = (30845.5 - 32500)/(3000/sqrt(20)) = -2.4664

p-value = 0.0137

alpha = 0.1
Reject null hypothesis

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

b)
H0: = 31,500
Ha: 31,500

test statistics, z = (30845.5 - 31500)/(3000/sqrt(20)) = -0.9757

p-value = 0.3292

alpha = 0.1
Failed to reject null hypothesis

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

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