Consider a paint-drying situation in which drying time for a test specimen is normally distributed with o = 6. The hypotheses Ho: u = 73 and H: H < 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 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. 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) =
Consider a paint-drying situation in which drying time for a test specimen is normally distributed with o = 6. The hypotheses Ho: u = 73 and H: H < 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 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. 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) =
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 σ = 6. The hypotheses \( H_0: \mu = 73 \) and \( H_a: \mu < 73 \) are to be tested using a random sample of n = 25 observations.
**(a)** How many standard deviations of \( \bar{X} \) below the null value is \( \bar{x} = 72.3 \)? (Round your answer to two decimal places.)
___ standard deviations
**(b)** If \( \bar{x} = 72.3 \), what is the conclusion using \( \alpha = 0.005 \)?
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.)
\[ z = \]
___
\[ P\text{-value} = \]
___
State the conclusion in the problem context.
- 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.
- 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 \( \alpha = 0.005 \), what is \( \beta(70) \)? (Round your answer to four decimal places.)
\( \beta(70) = \)
___
**(d)** If the test procedure with \( \alpha = 0.005 \) is used, what n is necessary to ensure that \( \beta(70) = 0.01 \)? (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 \( \mu = 76 \)? (Round your answer to four decimal places.)
___](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8edd889e-338a-4275-872c-5b2b400b4e22%2Fbbec7f5d-c9f1-43bd-84e3-b53cc8f5d9c3%2Fondeqqd_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 6. The hypotheses \( H_0: \mu = 73 \) and \( H_a: \mu < 73 \) are to be tested using a random sample of n = 25 observations.
**(a)** How many standard deviations of \( \bar{X} \) below the null value is \( \bar{x} = 72.3 \)? (Round your answer to two decimal places.)
___ standard deviations
**(b)** If \( \bar{x} = 72.3 \), what is the conclusion using \( \alpha = 0.005 \)?
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.)
\[ z = \]
___
\[ P\text{-value} = \]
___
State the conclusion in the problem context.
- 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.
- 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 \( \alpha = 0.005 \), what is \( \beta(70) \)? (Round your answer to four decimal places.)
\( \beta(70) = \)
___
**(d)** If the test procedure with \( \alpha = 0.005 \) is used, what n is necessary to ensure that \( \beta(70) = 0.01 \)? (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 \( \mu = 76 \)? (Round your answer to four decimal places.)
___
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