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Consider a paint-drying situation in which drying time for a test specimen is normally distributed with = 8. The hypotheses Ho: μ = 73 and H₂: < 73 are to be tested using a random sample of n = 25 observations (a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.) 0.44 ✔ standard deviations (b) If x = 72.3, what is the conclusion using a = 0.006? Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = -0.44 P-value = 0.3299 State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. O Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. ● Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. (c) For the test procedure with a = 0.006, what is (70)? (Round your answer to four decimal places.) B(70) = 0.2627 x (d) If the test procedure with a = 0.006 is used, what n is necessary to ensure that p(70) = 0.01? (Round your answer up to the next whole number.) n = 167 ✔specimens (e) If a level 0.01 test is used with n= 100, what is the probability of a type I error when = 76? (Round your answer to four decimal places.) 0.0000 ✓ You may need to use the appropriate table in the Appendix of Tables to answer this question.

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with = 8. The hypotheses Ho: μ = 73 and H₂: < 73 are to be tested using a random sample of n = 25 observations (a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.) 0.44 ✔ standard deviations (b) If x = 72.3, what is the conclusion using a = 0.006? Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = -0.44 P-value = 0.3299 State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. O Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. ● Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. (c) For the test procedure with a = 0.006, what is (70)? (Round your answer to four decimal places.) B(70) = 0.2627 x (d) If the test procedure with a = 0.006 is used, what n is necessary to ensure that p(70) = 0.01? (Round your answer up to the next whole number.) n = 167 ✔specimens (e) If a level 0.01 test is used with n= 100, what is the probability of a type I error when = 76? (Round your answer to four decimal places.) 0.0000 ✓ You may need to use the appropriate table in the Appendix of Tables to answer this question.

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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Consider a paint-drying situation in which drying time for a test specimen is normally distributed with = 8. The hypotheses Ho: μ = 73 and H₂: μ< 73 are to be tested using a random sample of n = 25 observations. (a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.) 0.44 standard deviations (b) If x = 72.3, what is the conclusion using a = 0.006? Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = -0.44 P-value = 0.3299 State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. O Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. (c) For the test procedure with a = 0.006, what is ß(70)? (Round your answer to four decimal places.) B(70) = 0.2627 X (d) If the test procedure with a = 0.006 is used, what n is necessary to ensure that p(70) = 0.01? (Round your answer up to the next whole number.) n = 167 specimens (e) If a level 0.01 test is used with n = 100, what is the probability of a type I error when μ = 76? (Round your answer to four decimal places.) 0.0000 You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:Consider a paint-drying situation in which drying time for a test specimen is normally distributed with = 8. The hypotheses Ho: μ = 73 and H₂: μ< 73 are to be tested using a random sample of n = 25 observations. (a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.) 0.44 standard deviations (b) If x = 72.3, what is the conclusion using a = 0.006? Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = -0.44 P-value = 0.3299 State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. O Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. (c) For the test procedure with a = 0.006, what is ß(70)? (Round your answer to four decimal places.) B(70) = 0.2627 X (d) If the test procedure with a = 0.006 is used, what n is necessary to ensure that p(70) = 0.01? (Round your answer up to the next whole number.) n = 167 specimens (e) If a level 0.01 test is used with n = 100, what is the probability of a type I error when μ = 76? (Round your answer to four decimal places.) 0.0000 You may need to use the appropriate table in the Appendix of Tables to answer this question.
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