Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 8. The hypotheses Ho: =74 and Ha: <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.) 1.06 standard deviations (b) If x=72.3, what is the conclusion using a = 0.003? 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 = -1.06 P-value = 0.1446 State the conclusion in the problem context. Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. (c) For the test procedure with a = 0.003, what is ẞ(70)? (Round your answer to four decimal places.) ẞ(70) = 0.4013 (d) If the test procedure with a = 0.003 is used, what n is necessary to ensure that ẞ(70) = 0.01? (Round your answer up to the next whole number.) x specimens n = 2208 (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.)
Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 8. The hypotheses Ho: =74 and Ha: <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.) 1.06 standard deviations (b) If x=72.3, what is the conclusion using a = 0.003? 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 = -1.06 P-value = 0.1446 State the conclusion in the problem context. Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74. Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74. (c) For the test procedure with a = 0.003, what is ẞ(70)? (Round your answer to four decimal places.) ẞ(70) = 0.4013 (d) If the test procedure with a = 0.003 is used, what n is necessary to ensure that ẞ(70) = 0.01? (Round your answer up to the next whole number.) x specimens n = 2208 (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.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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Transcribed Image Text:Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 8. The hypotheses Ho: =74 and Ha: <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.)
1.06
standard deviations
(b) If x=72.3, what is the conclusion using a = 0.003?
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 = -1.06
P-value = 0.1446
State the conclusion in the problem context.
Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74.
Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74.
Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74.
Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74.
(c) For the test procedure with a = 0.003, what is ẞ(70)? (Round your answer to four decimal places.)
ẞ(70) = 0.4013
(d) If the test procedure with a = 0.003 is used, what n is necessary to ensure that ẞ(70) = 0.01? (Round your answer up to the next whole number.)
x specimens
n = 2208
(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.)
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