For problem 10, 11, and 12 below: (i) State the requirement (ii) State the null and alternative hypotheses with the correct symbols (iii) Write all the statistics (iv) Write the formula of the test statistic and find the test statistic (you may use a calculator, but you are required to write down the command and all the numbers you enter) (v) Find the critical value or the P-value (you may use a calculator, but you are required to write down the command and all the numbers you enter) (vi) Decide to reject or fail to reject Ho and explain the reason (vii) Wording the conclusion (vii) Answer the question based on your result above 10. Use the P-value method to test the claim that for the adult population of one town, the mean annual salary is $30,000. Sample data are summarized as n = 17, T = $22,300 and s = $14,200. Use a significance level of a = 0.05. Is the assumption correct? 11. A manufacturer uses a new production method to produce steel rods. A sample of 17 steel rods resulted in lengths with a standard deviation of 4.7 cm. At the 0.10 significance level, use the critical value method to test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method. Is it possible to say that the new method produces longer rods? 12. Let the sample size of leg strengths be 7 and the sample mean and sample standard deviation be 315 watts and 16 watts, respectively. (a) Is there evidence that leg strength exceeds 300 watts at significance level 0.05? Find the P-value. (b) Compute the power of the test if the true strength is 305 watts. (c) What sample size would be required to detect a true mean of 305 watts if the power of the test should be at least 0.9?
For problem 10, 11, and 12 below: (i) State the requirement (ii) State the null and alternative hypotheses with the correct symbols (iii) Write all the statistics (iv) Write the formula of the test statistic and find the test statistic (you may use a calculator, but you are required to write down the command and all the numbers you enter) (v) Find the critical value or the P-value (you may use a calculator, but you are required to write down the command and all the numbers you enter) (vi) Decide to reject or fail to reject Ho and explain the reason (vii) Wording the conclusion (vii) Answer the question based on your result above 10. Use the P-value method to test the claim that for the adult population of one town, the mean annual salary is $30,000. Sample data are summarized as n = 17, T = $22,300 and s = $14,200. Use a significance level of a = 0.05. Is the assumption correct? 11. A manufacturer uses a new production method to produce steel rods. A sample of 17 steel rods resulted in lengths with a standard deviation of 4.7 cm. At the 0.10 significance level, use the critical value method to test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method. Is it possible to say that the new method produces longer rods? 12. Let the sample size of leg strengths be 7 and the sample mean and sample standard deviation be 315 watts and 16 watts, respectively. (a) Is there evidence that leg strength exceeds 300 watts at significance level 0.05? Find the P-value. (b) Compute the power of the test if the true strength is 305 watts. (c) What sample size would be required to detect a true mean of 305 watts if the power of the test should be at least 0.9?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:For problem 10, 11, and 12 below:
(i) State the requirement
(ii) State the null and alternative hypotheses with the correct symbols
(iii) Write all the statistics
(iv) Write the formula of the test statistic and find the test statistic (you may use a calculator, but
you are required to write down the command and all the numbers you enter)
(v) Find the critical value or the P-value (you may use a calculator, but you are required to write
down the command and all the numbers you enter)
(vi) Decide to reject or fail to reject Ho and explain the reason
(vii) Wording the conclusion
(viii) Answer the question based on your result above
10. Use the P-value method to test the claim that for the adult population of one town, the
mean annual salary is $30,000. Sample data are summarized as n = 17, T = $22,300
and s = $14,200. Use a significance level of a = 0.05. Is the assumption correct?
11. A manufacturer uses a new production method to produce steel rods. A sample of 17
steel rods resulted in lengths with a standard deviation of 4.7 cm. At the 0.10 significance
level, use the critical value method to test the claim that the new production method has
lengths with a standard deviation different from 3.5 cm, which was the standard deviation
for the old method. Is it possible to say that the new method produces longer rods?
12. Let the sample size of leg strengths be 7 and the sample mean and sample standard
deviation be 315 watts and 16 watts, respectively.
(a) Is there evidence that leg strength exceeds 300 watts at significance level 0.05? Find
the P-value.
(b) Compute the power of the test if the true strength is 305 watts.
(c) What sample size would be required to detect a true mean of 305 watts if the power
of the test should be at least 0.9?
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