Consider a paint-drying situation in which drying time for a test specimen is normally distributed with o = 6. The hypotheses H: µ = 74 and H: µ < 74 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 = 0.004? 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. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. O Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. (c) For the test procedure with a = 0.004, what is B(70)? (Round your answer to four decimal places.) B(70) = (d) If the test procedure with a = 0.004 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.)
Consider a paint-drying situation in which drying time for a test specimen is normally distributed with o = 6. The hypotheses H: µ = 74 and H: µ < 74 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 = 0.004? 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. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. O Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. (c) For the test procedure with a = 0.004, what is B(70)? (Round your answer to four decimal places.) B(70) = (d) If the test procedure with a = 0.004 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.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Transcribed Image Text:Consider a paint-drying situation in which drying time for a test specimen is normally distributed with o = 6. The hypotheses H: µ = 74 and H: µ < 74 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 = 0.004?
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.
O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74.
O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74.
O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74.
O Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74.
(c) For the test procedure with a = 0.004, what is B(70)? (Round your answer to four decimal places.)
B(70) =
(d) If the test procedure with a = 0.004 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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