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1) We need a sample proportion, p and a sample size, n. 2) We need to make sure that a normal model is appropriate for the underlying sampling distribution. To do so, we check that np > 10 and n(1- p) > 10. These conditions state that we are expecting at least 10 successes and failures given the proportion and the sample size that we're dealing with. p(1-p). 3) We need a standard error (based on the sample proportion and the sample size), SE = 4) Next, we need a critical z-score, z* 5) The margin of error is calculated as MOE = z* × SE- The confidence interval is calculated as Lower Bound = p – z* × SE Upper Bound = p+ z* × SE This is the same as Lower Bound = p – MOE Upper Bound = p+ MOE %3D (A) In a chili cookoff, 66 people sample all of the chili and 30% vote to give the "Fire Hot Mouth Burner" the best chili in the contest. Since we haven't sampled everyone at the entire cook off we have to use a confidence interval to estimate the proportion of chili eating contest-goers that might choose this as the best chili of the contest. (1) p = (ii) n = (ii) np = (iv) n(1 – p) = (this is the number that voted for the "Fire Hot Mouth Burner") (this is the number that didn't vote for the "Fire Hot Mouth Burner") (v) Since both of the previous answers are greater than or equal to 10 we can proceed with a normal model for the confidence interval. We now need to get the critical z-score. We will use a 99% confidence level. In MS Excel we need to use the "=norm.s.inv()" command to determine the appropriate critical z-score. =norm.s.inv(

1) We need a sample proportion, p and a sample size, n. 2) We need to make sure that a normal model is appropriate for the underlying sampling distribution. To do so, we check that np > 10 and n(1- p) > 10. These conditions state that we are expecting at least 10 successes and failures given the proportion and the sample size that we're dealing with. p(1-p). 3) We need a standard error (based on the sample proportion and the sample size), SE = 4) Next, we need a critical z-score, z* 5) The margin of error is calculated as MOE = z* × SE- The confidence interval is calculated as Lower Bound = p – z* × SE Upper Bound = p+ z* × SE This is the same as Lower Bound = p – MOE Upper Bound = p+ MOE %3D (A) In a chili cookoff, 66 people sample all of the chili and 30% vote to give the "Fire Hot Mouth Burner" the best chili in the contest. Since we haven't sampled everyone at the entire cook off we have to use a confidence interval to estimate the proportion of chili eating contest-goers that might choose this as the best chili of the contest. (1) p = (ii) n = (ii) np = (iv) n(1 – p) = (this is the number that voted for the "Fire Hot Mouth Burner") (this is the number that didn't vote for the "Fire Hot Mouth Burner") (v) Since both of the previous answers are greater than or equal to 10 we can proceed with a normal model for the confidence interval. We now need to get the critical z-score. We will use a 99% confidence level. In MS Excel we need to use the "=norm.s.inv()" command to determine the appropriate critical z-score. =norm.s.inv(

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1) We need a sample proportion, p and a sample size, n. 2) We need to make sure that a normal model is appropriate for the underlying sampling distribution. To do so, we check that np > 10 and n(1- p) 2 10. These conditions state that we are expecting at least 10 successes and failures given the proportion and the sample size that we're | dealing with. P(1-p) 3) We need a standard error (based on the sample proportion and the sample size), SE 4) Next, we need a critical z-score, z* 5) The margin of error is calculated as MOE z* x SE- The confidence interval is calculated as Lower Bound = p – z* × SE Upper Bound = p+ z* × SE This is the same as Lower Bound —р— МОЕ Upper Bound = p+ MOE %3D - (A) In a chili cookoff, 66 people sample all of the chili and 30% vote to give the "Fire Hot Mouth Burner" the best chili in the contest. Since we haven't sampled everyone at the entire cook off we have to use a confidence interval to estimate the proportion of chili eating contest-goers that might choose this as the best chili of the contest. (1) P (ii) n = (ii) nộ (w) п(1 — р) — (this is the number that voted for the "Fire Hot Mouth Burner") (this is the number that didn't vote for the "Fire Hot Mouth Burner") (v) Since both of the previous answers are greater than or equal to 10 we can proceed with a normal model for the confidence interval. We now need to get the critical z-score. We will use a 99% confidence level. In MS Excel we need to use the "=norm.s.inv()" command to determine the appropriate critical z-score. =norm.s.inv(
Transcribed Image Text:1) We need a sample proportion, p and a sample size, n. 2) We need to make sure that a normal model is appropriate for the underlying sampling distribution. To do so, we check that np > 10 and n(1- p) 2 10. These conditions state that we are expecting at least 10 successes and failures given the proportion and the sample size that we're | dealing with. P(1-p) 3) We need a standard error (based on the sample proportion and the sample size), SE 4) Next, we need a critical z-score, z* 5) The margin of error is calculated as MOE z* x SE- The confidence interval is calculated as Lower Bound = p – z* × SE Upper Bound = p+ z* × SE This is the same as Lower Bound —р— МОЕ Upper Bound = p+ MOE %3D - (A) In a chili cookoff, 66 people sample all of the chili and 30% vote to give the "Fire Hot Mouth Burner" the best chili in the contest. Since we haven't sampled everyone at the entire cook off we have to use a confidence interval to estimate the proportion of chili eating contest-goers that might choose this as the best chili of the contest. (1) P (ii) n = (ii) nộ (w) п(1 — р) — (this is the number that voted for the "Fire Hot Mouth Burner") (this is the number that didn't vote for the "Fire Hot Mouth Burner") (v) Since both of the previous answers are greater than or equal to 10 we can proceed with a normal model for the confidence interval. We now need to get the critical z-score. We will use a 99% confidence level. In MS Excel we need to use the "=norm.s.inv()" command to determine the appropriate critical z-score. =norm.s.inv(
(vi) This gives a critical z-score of (vii) The standard error is: SE = (viii) The margin of error is: МОЕ — (ix) Hence, we are 99% confident that the true proportion of people that will vote for "Fire Hot Mouth Burner" is between and (B) In a hospital, an orthopedic doctor collects a random sample of 63 previous patients and checks to see if pre-surgical physical therapy strength training helps to speed their recovery after a total hip replacement. She finds that in 69.84% of the 63 patients that indeed it does. Since the doctor didn't sample every possible surgical patient she has to use a confidence interval to estimate the proportion of total hip surgical patients that will benefit from pre-surgical PT. (1) P (ii) n = (ii) nộ = (iv) n(1 – p) (this is the number showed improved recovery time.) (this is the number that didn't show improved recovery time.) (v) Since both of the previous answers are greater than or equal to 10 we can proceed with a normal model for the confidence interval. We now need to get the critical z-score. We will use a 94% confidence level. In MS Excel we need to use the "=norm.s.inv()" command to determine the appropriate critical z-score. =norm.s.inv( (vi) This gives a critical z-score of (vii) The standard error is: SE (vii) The margin of error is: МОЕ — (ix) Hence, we are 99% confident that the true proportion of surgical total hip patients that will have improved recovery time with pre-surgical PT is between and
Transcribed Image Text:(vi) This gives a critical z-score of (vii) The standard error is: SE = (viii) The margin of error is: МОЕ — (ix) Hence, we are 99% confident that the true proportion of people that will vote for "Fire Hot Mouth Burner" is between and (B) In a hospital, an orthopedic doctor collects a random sample of 63 previous patients and checks to see if pre-surgical physical therapy strength training helps to speed their recovery after a total hip replacement. She finds that in 69.84% of the 63 patients that indeed it does. Since the doctor didn't sample every possible surgical patient she has to use a confidence interval to estimate the proportion of total hip surgical patients that will benefit from pre-surgical PT. (1) P (ii) n = (ii) nộ = (iv) n(1 – p) (this is the number showed improved recovery time.) (this is the number that didn't show improved recovery time.) (v) Since both of the previous answers are greater than or equal to 10 we can proceed with a normal model for the confidence interval. We now need to get the critical z-score. We will use a 94% confidence level. In MS Excel we need to use the "=norm.s.inv()" command to determine the appropriate critical z-score. =norm.s.inv( (vi) This gives a critical z-score of (vii) The standard error is: SE (vii) The margin of error is: МОЕ — (ix) Hence, we are 99% confident that the true proportion of surgical total hip patients that will have improved recovery time with pre-surgical PT is between and
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