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Consider a paint-drying situation in which drying time for a test specimen normally distributed with o = 7. The hypotheses Ho: u = 73 and H: u < 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.) standard deviations (b) If x = 72.3, what is the conclusion using a = 0.005? 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.) P-value = State the conclusion in the problem context. • Do not 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 Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. O Do not reject the null hypothesis. There sufficient evidence to conclude that the mean drying time is less than 73. (e) For the test procedure vith a = 0.005, vhat is B(70)? (Round vour answer to four decimal places.)

Consider a paint-drying situation in which drying time for a test specimen normally distributed with o = 7. The hypotheses Ho: u = 73 and H: u < 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.) standard deviations (b) If x = 72.3, what is the conclusion using a = 0.005? 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.) P-value = State the conclusion in the problem context. • Do not 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 Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 73. O Do not reject the null hypothesis. There sufficient evidence to conclude that the mean drying time is less than 73. (e) For the test procedure vith a = 0.005, vhat is B(70)? (Round vour answer to four decimal places.)

A First Course in Probability (10th Edition)
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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Consider a paint-drying situation in which drying time for a test specimen is normally distributed with o = 7. The hypotheses H,: u = 73 and H: u < 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.) standard deviations (b) If x = 72.3, what is the conclusion using a = 0.005? 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 = P-value = State the conclusion in the problem context. O Do not 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 Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time less than 73. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. (c) For the test procedure with a = 0.005, what is B(70)? (Round your answer to four decimal places.) B(70) = (d) If the test procedure with a = 0.005 is used, what n is necessary to ensure that B(70) = 0.01? (Round your answer up to the next whole number.) n = specimens (e) If a level 0.01 test is used with n = 100, what is the probability of a type I error when u = 76? (Round your answer to four decimal places.)
Transcribed Image Text:Consider a paint-drying situation in which drying time for a test specimen is normally distributed with o = 7. The hypotheses H,: u = 73 and H: u < 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.) standard deviations (b) If x = 72.3, what is the conclusion using a = 0.005? 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 = P-value = State the conclusion in the problem context. O Do not 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 Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time less than 73. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 73. (c) For the test procedure with a = 0.005, what is B(70)? (Round your answer to four decimal places.) B(70) = (d) If the test procedure with a = 0.005 is used, what n is necessary to ensure that B(70) = 0.01? (Round your answer up to the next whole number.) n = specimens (e) If a level 0.01 test is used with n = 100, what is the probability of a type I error when u = 76? (Round your answer to four decimal places.)
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