Use Calc > Calculator to calculate the LCL and the UCL based on sample size n...
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Use Calc > Calculator to calculate the LCL and the UCL based on sample size n = 100 and the sample proportions that are stored in Column pgen2. For LCL, calculate the expression pgen2 - 1.960*(pgen2*(1 - pgen2)/100)**.5 and place the values in Column LCL2. In a similar manner, calculate the UCL's using expression pgen2 + 1.960*(pgen2*(1 - pgen2)/100)**.5 and place them in Column UCL2. Copy the values xgen2, pgen2, LCL2 and UCL2 from your first 10 CI's of your MTB computer worksheet into columns 2 - 5 of Table 2 below and indicate in column 6 whether the CI covers the population rate p = .04. (Use two decimal places for pgen2 and three decimal places for LCL2 and UCL2.) Table 2. CI results for p= .04 (n = 100) Normal theory CI Sample xgen2 pgen2 LCL2 UCL2 1 2 3 4 5 6 7 8 9 10 Cover .04? (Yes or No) Sample size n 100 100 For the first row of Table 2, enter the values as responses to questions 17 and 18: Parameter value p .30 .04 17. xgen2= 18. pgen2= Now we will check all 1,000 samples to see in how many cases the CI covers p = .04. Use Calc> Calculator and the statement sum(LCL2<.04 and .04 <UCL2) to determine the number of CI's that covered p. Put the result into column Coverage2. Express the result as a percentage. 20. Coverage- For LON-CAPA submission, enter a number between 0 and 100 without % symbol. 19. Out of the first 10 intervals. recorded in Table 2, how many cover .04? E. Summarize your findings below in Table 3. Table 3. Summary of coverage results for 95% CI's for p calculated from 1,000 random samples of size n=100 Observed coverage % by normal theory CI Does the CI deliver close to 95% coverage rate for p=0.30, while the coverage rate for p=0.04 is quite a bit lower than the advertised 95%? Conclusion: Do not use the normal theory confidence interval for estimating p if you suspect p is very small, that is, you are sampling for a rare attribute (unless n is quite large). The normal theory confidence interval is equally untrustworthy if p is near one. The practical rule of when normal theory confidence interval for p can be used is: both n p and n(1-p) should be at least 10 (some authors say that these quantities need to be at least 5, see p. 385 of the text). Other methods of constructing confidence interval for the population proportion are available but are outside of the scope of this introductory course. Use Calc > Calculator to calculate the LCL and the UCL based on sample size n = 100 and the sample proportions that are stored in Column pgen2. For LCL, calculate the expression pgen2 - 1.960*(pgen2*(1 - pgen2)/100)**.5 and place the values in Column LCL2. In a similar manner, calculate the UCL's using expression pgen2 + 1.960*(pgen2*(1 - pgen2)/100)**.5 and place them in Column UCL2. Copy the values xgen2, pgen2, LCL2 and UCL2 from your first 10 CI's of your MTB computer worksheet into columns 2 - 5 of Table 2 below and indicate in column 6 whether the CI covers the population rate p = .04. (Use two decimal places for pgen2 and three decimal places for LCL2 and UCL2.) Table 2. CI results for p= .04 (n = 100) Normal theory CI Sample xgen2 pgen2 LCL2 UCL2 1 2 3 4 5 6 7 8 9 10 Cover .04? (Yes or No) Sample size n 100 100 For the first row of Table 2, enter the values as responses to questions 17 and 18: Parameter value p .30 .04 17. xgen2= 18. pgen2= Now we will check all 1,000 samples to see in how many cases the CI covers p = .04. Use Calc> Calculator and the statement sum(LCL2<.04 and .04 <UCL2) to determine the number of CI's that covered p. Put the result into column Coverage2. Express the result as a percentage. 20. Coverage- For LON-CAPA submission, enter a number between 0 and 100 without % symbol. 19. Out of the first 10 intervals. recorded in Table 2, how many cover .04? E. Summarize your findings below in Table 3. Table 3. Summary of coverage results for 95% CI's for p calculated from 1,000 random samples of size n=100 Observed coverage % by normal theory CI Does the CI deliver close to 95% coverage rate for p=0.30, while the coverage rate for p=0.04 is quite a bit lower than the advertised 95%? Conclusion: Do not use the normal theory confidence interval for estimating p if you suspect p is very small, that is, you are sampling for a rare attribute (unless n is quite large). The normal theory confidence interval is equally untrustworthy if p is near one. The practical rule of when normal theory confidence interval for p can be used is: both n p and n(1-p) should be at least 10 (some authors say that these quantities need to be at least 5, see p. 385 of the text). Other methods of constructing confidence interval for the population proportion are available but are outside of the scope of this introductory course.
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Related Book For
Statistics for Business and Economics
ISBN: 978-0134506593
13th edition
Authors: James T. McClave, P. George Benson, Terry Sincich
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