Homework Sourse23 How heavy a load pounds is needed to pull apart pieces of
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 |
Solution
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]
