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The calibration of a scale is to be checked by weighing a 15 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? O Hoi H= 15 ST > H :°H O Ho: H = 15 HiH = 15 O Hoi H = 15 H:H< 15 O Ho: H = 15 H: µ = 15 O Hoi H = 15 HgiH> 15 (b) With the sample mean itself as the test statistic, what is the P-value when x = 14.83? (Round your answer to four decimal places.) 0.00002 What would you conclude at significance level 0.01? O Conclude that the true mean measured weight differs from 15 kg. O Conclude that the true mean measured weight is the same as 15 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact µ = 15.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 14.9? (Round your answer to four decimal places.) 0.0801

The calibration of a scale is to be checked by weighing a 15 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? O Hoi H= 15 ST > H :°H O Ho: H = 15 HiH = 15 O Hoi H = 15 H:H< 15 O Ho: H = 15 H: µ = 15 O Hoi H = 15 HgiH> 15 (b) With the sample mean itself as the test statistic, what is the P-value when x = 14.83? (Round your answer to four decimal places.) 0.00002 What would you conclude at significance level 0.01? O Conclude that the true mean measured weight differs from 15 kg. O Conclude that the true mean measured weight is the same as 15 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact µ = 15.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 14.9? (Round your answer to four decimal places.) 0.0801

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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The calibration of a scale is to be checked by weighing a 15 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ο Hg: μ + 15 H: H < 15 Ο H: μ + 15 Hg:H = 15 Ο H9: μ= 15 H,: μ< 15 Ο H: μ= 15 H: H = 15 Ο H: μ= 15 H: H > 15 (b) with the sample mean itself as the test statistic, what is the P-value when x = 14.83? (Round your answer to four decimal places.) 0.00002 What would you conclude at significance level 0.01? O Conclude that the true mean measured weight differs from 15 kg. O Conclude that the true mean measured weight is the same as 15 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 15.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 14.9? (Round your answer to four decimal places.) 0.0801
Transcribed Image Text:The calibration of a scale is to be checked by weighing a 15 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ο Hg: μ + 15 H: H < 15 Ο H: μ + 15 Hg:H = 15 Ο H9: μ= 15 H,: μ< 15 Ο H: μ= 15 H: H = 15 Ο H: μ= 15 H: H > 15 (b) with the sample mean itself as the test statistic, what is the P-value when x = 14.83? (Round your answer to four decimal places.) 0.00002 What would you conclude at significance level 0.01? O Conclude that the true mean measured weight differs from 15 kg. O Conclude that the true mean measured weight is the same as 15 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 15.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 14.9? (Round your answer to four decimal places.) 0.0801
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