A paint company has developed a new paint formula which should have a faster drying time compared to the old formula. Paint drying time is known to be normally distributed, and from previous tests it is known that the original paint formula has a mean drying time of μ₁ = 45 min (0₁ = 6 min). The company's R&D scientists believe the new formula will have a mean drying time of #₂ = 35 min (0₂= 4 min) (that is, they expect the new formula to dry an average of 10 min faster than the old formula, or that #₁ - 2 = 10). A scientist takes 16 samples of each paint formula and determines the mean drying time for each batch to be X₁ = 44 min and X₂ = 36 min, respectively. Does the assumed value of μ₂ = 35 min seem correct? (That is, does #₁ #2 = 10 min seem correct if he finds ₁-X₂ = 8?) i) ii) How likely is it to find samples as extreme as (or more extreme than) these? (That is, what is P(X₁X₂ <8), under the assumption that μ₂ = 35?) Does the assumed value of #2 = 35 min seem correct? (That is, is ₁ - 2 = 10 likely to be correct if he finds X₁ X₂ = 8?) Circle YES or NO and briefly explain your answer. YES NO
A paint company has developed a new paint formula which should have a faster drying time compared to the old formula. Paint drying time is known to be normally distributed, and from previous tests it is known that the original paint formula has a mean drying time of μ₁ = 45 min (0₁ = 6 min). The company's R&D scientists believe the new formula will have a mean drying time of #₂ = 35 min (0₂= 4 min) (that is, they expect the new formula to dry an average of 10 min faster than the old formula, or that #₁ - 2 = 10). A scientist takes 16 samples of each paint formula and determines the mean drying time for each batch to be X₁ = 44 min and X₂ = 36 min, respectively. Does the assumed value of μ₂ = 35 min seem correct? (That is, does #₁ #2 = 10 min seem correct if he finds ₁-X₂ = 8?) i) ii) How likely is it to find samples as extreme as (or more extreme than) these? (That is, what is P(X₁X₂ <8), under the assumption that μ₂ = 35?) Does the assumed value of #2 = 35 min seem correct? (That is, is ₁ - 2 = 10 likely to be correct if he finds X₁ X₂ = 8?) Circle YES or NO and briefly explain your answer. YES NO
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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use a cutoff value of 5%.
Transcribed Image Text:b) A paint company has developed a new paint formula which should have a faster drying time
compared to the old formula. Paint drying time is known to be normally distributed, and
from previous tests it is known that the original paint formula has a mean drying time of
H4₁ = 45 min (0₁ = 6 min). The company's R&D scientists believe the new formula will have
a mean drying time of μ₂ = 35 min (0₂ = 4 min) (that is, they expect the new formula to dry
an average of 10 min faster than the old formula, or that #₁ - 2 = 10).
A scientist takes 16 samples of each paint formula and determines the mean drying time for
each batch to be X₁ = 44 min and X₂ = 36 min, respectively. Does the assumed value of μ₂ =
35 min seem correct? (That is, does ₁ - ₂ = 10 min seem correct if he finds X₁ X₂ = 8?)
i) How likely is it to find samples as extreme as (or more extreme than) these?
(That is, what is P(X₁ X₂ < 8), under the assumption that µ₂ = 35?)
ii)
Does the assumed value of μ₂ = 35 min seem correct? (That is, is ₁ - ₂ = 10 likely
to be correct if he finds X₁ X₂ = 8?) Circle YES or NO and briefly explain your
answer.
YES
NO
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