The drying time of a certa n typef paint under spec fied test conditiors is «no

Question

The drying time of a certa n typef paint under spec fied test conditiors is «no n to be norm elly distributed with mean value 75 min and standard dev ation 9 min. Chern sts have proposed à e addit ve de gned to decrease average drying time, t is believed that drying times with this additive ill e ain or maly distributed with 9 Be ause of the expense asso iated with the additive, evidence should strong' ggest an improvement in a erage drying time before such a o nclusion is adopted Let denote the e ave age drying time when the additive is used. The appropriate hypotheses are Ha: -75 versus H·P

Explanation / Answer

a) Beta is the probability of type II error

i)

ii)

iii)

b)

z = (74 - 75)/(9/sqrt(2500)) = -5.55
p-value = 0.000

Reject the null hypothesis

No, Option (C)

mu0 (hypothesised mean) 75 sigma 9 n 121 alpha 0.01 sample/true mean 74 Std. Error. SE = sigma/sqrt(n) 0.8182 Zcritical -2.576 Xcritical values 72.89 Beta or type II error is the probability of fail to reject the null hypothesis P(X<72.89|mu=74) 0.08793 Hence type II error probability is 0.0879 Power of the test 0.9121

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