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

Question

23. 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?

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.)

Pvalue =______

(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 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 = __________

You may need to use the appropriate Appendix Table to answer this question. http://www.webassign.net/mbasicstat6/appendix-tables.pdf

33,220     31,910     32,620     26,540     33,330     32,300     33,020     32,030     30,410     32,720     23,060     30,950     32,770     33,660     32,310     24,070     30,150     31,250     28,680     31,910    

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   32500  
Ha:    u   =/   32500  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    30845.5          
uo = hypothesized mean =    32500          
n = sample size =    20          
s = standard deviation =    3000          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.466382979 [ANSWER, TEST STATISTIC]

********************          
              
Also, the p value is, as it is two tailed,              
              
p =    0.013648532   [ANSWER, P VALUE]

*******************      
              
Thus, as P < 0.10, there is statistically significant evidence at the = 0.10 level against the hypothesis that the mean is 32,500 pounds. [CONCLUSION]

********************************

b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   31500  
Ha:    u   =/   31500  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    30845.5          
uo = hypothesized mean =    31500          
n = sample size =    20          
s = standard deviation =    3000          
              
Thus, z = (X - uo) * sqrt(n) / s =    -0.975670994 [ANSWER, TEST STATISTIC]          
              
Also, the p value is              
              
p =    0.329227531   [ANSWER, P VALUE]      
              

Thus, as P > 0.10, there is no statistically significant evidence at the = 0.10 level against the hypothesis that the mean is 32,500 pounds. [CONCLUSION]      
              

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