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.

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 =

(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

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 =

33,240     31,880     32,600     26,530     33,300     32,280     33,000     32,010     30,410     32,740     23,050     30,970     32,680     33,610     32,290     24,000     30,140     31,330     28,780     31,870    

Explanation / Answer

Null Hypothesis:

H0: = 31,500

Alternative Hypothesis;

Ha: 31,500

Test statistic:

x = 30835.5 , s = 3000 , n = 20 , mean = 31500

z = (x - mean) / ( s / sqrt(n))

= ( 30835.5 - 31500) / ( 3000/sqrt(20))

= -0.99

Now, we need to find p value using z = -0.99

p value = 0.3222

As p value is greater than significance level 0.10

So, we fail to reject the null hypothesis

there is not statistically significant evidence at the = 0.10 level against the hypothesis that the mean is 31,500 pounds for the two-sided alternative

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