Practice 7. The drying time of a certain type of paint under specified test conditions is known to be normally distributed with mean value 30 min and standard deviation 3 min. Chemists have proposed a new additive designed to decrease average drying time. Because of the expense associated with the additive, evidence should strongly suggest an improvement in average drying time before such a conclusion is adopted. Experimental data consists of drying times from n = 49 test specimens. (a) From the sample, it is given that test the following hypothesis against its alternative.: = 1440.6. Using the significance level a = 0.01, Ho : μ = 30, US Ha : μ < 30. (b) State the type I and II errors in the context of the problem. (c) Find the type II error rate of the test in (a) when a = 29.

MATLAB: An Introduction with Applications
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Practice 7. The drying time of a certain type of paint under specified test conditions is
known to be normally distributed with mean value 30 min and standard deviation 3 min.
Chemists have proposed a new additive designed to decrease average drying time. Because of
the expense associated with the additive, evidence should strongly suggest an improvement
in average drying time before such a conclusion is adopted. Experimental data consists of
drying times from n = 49 test specimens.
=
(a) From the sample, it is given that ₁x 1440.6. Using the significance level a = 0.01,
test the following hypothesis against its alternative.:
Ho : | = 30, US
Ha : μ < 30.
(b) State the type I and II errors in the context of the problem.
(c) Find the type II error rate of the test in (a) when μla = 29.
Transcribed Image Text:Practice 7. The drying time of a certain type of paint under specified test conditions is known to be normally distributed with mean value 30 min and standard deviation 3 min. Chemists have proposed a new additive designed to decrease average drying time. Because of the expense associated with the additive, evidence should strongly suggest an improvement in average drying time before such a conclusion is adopted. Experimental data consists of drying times from n = 49 test specimens. = (a) From the sample, it is given that ₁x 1440.6. Using the significance level a = 0.01, test the following hypothesis against its alternative.: Ho : | = 30, US Ha : μ < 30. (b) State the type I and II errors in the context of the problem. (c) Find the type II error rate of the test in (a) when μla = 29.
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