7. The drying time of a type of paint under specified test conditions is known to be normally distributed with a mean value of 75 min and a standard deviation of 9 min. Chemists have proposed a new additive desinged to decrease average drying time. It is believed that drying times with this additive will remain normally distributed with o = 9. Because of the expense associated with the additive, evidence should strongly suggest an improvement in average dry- ing time before such a conclusion is adopted. Let u denote the true average drying time when the additive is used. The appropriate hypotheses are Ho : µ = 75 versus Ha : u < 75. Suppose that we take a sample of n = 25 test specimens. We would reject the null hypothesis if the sample mean from this sample is less than 71.5 minutes. (a) Find the value of a, the probability of a type I error, for this test. (b) of μ = 70. Find the value of B(70), the probability of a type II error when the true value
7. The drying time of a type of paint under specified test conditions is known to be normally distributed with a mean value of 75 min and a standard deviation of 9 min. Chemists have proposed a new additive desinged to decrease average drying time. It is believed that drying times with this additive will remain normally distributed with o = 9. Because of the expense associated with the additive, evidence should strongly suggest an improvement in average dry- ing time before such a conclusion is adopted. Let u denote the true average drying time when the additive is used. The appropriate hypotheses are Ho : µ = 75 versus Ha : u < 75. Suppose that we take a sample of n = 25 test specimens. We would reject the null hypothesis if the sample mean from this sample is less than 71.5 minutes. (a) Find the value of a, the probability of a type I error, for this test. (b) of μ = 70. Find the value of B(70), the probability of a type II error when the true value
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Please help with 7 a, and b
![7. The drying time of a type of paint under specified test conditions is known to be normally
distributed with a mean value of 75 min and a standard deviation of 9 min. Chemists have
proposed a new additive desinged to decrease average drying time. It is believed that drying
times with this additive will remain normally distributed with o = 9. Because of the expense
associated with the additive, evidence should strongly suggest an improvement in average dry-
ing time before such a conclusion is adopted. Let u denote the true average drying time when
the additive is used. The appropriate hypotheses are Ho : u = 75 versus Ha :µ < 75.
а
Suppose that we take a sample of n = 25 test specimens. We would reject the null hypothesis
if the sample mean a from this sample is less than 71.5 minutes.
(a)
Find the value of a, the probability of a type I error, for this test.
(b)
of μ - 70.
Find the value of B(70), the probability of a type II error when the true value](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f2030df-489c-4c06-8af8-a0bb3fa2ff8f%2Ff1dbba7e-715f-4b82-ba67-80d636a8b18c%2Fsdgv0ao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. The drying time of a type of paint under specified test conditions is known to be normally
distributed with a mean value of 75 min and a standard deviation of 9 min. Chemists have
proposed a new additive desinged to decrease average drying time. It is believed that drying
times with this additive will remain normally distributed with o = 9. Because of the expense
associated with the additive, evidence should strongly suggest an improvement in average dry-
ing time before such a conclusion is adopted. Let u denote the true average drying time when
the additive is used. The appropriate hypotheses are Ho : u = 75 versus Ha :µ < 75.
а
Suppose that we take a sample of n = 25 test specimens. We would reject the null hypothesis
if the sample mean a from this sample is less than 71.5 minutes.
(a)
Find the value of a, the probability of a type I error, for this test.
(b)
of μ - 70.
Find the value of B(70), the probability of a type II error when the true value
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