The focus of a human eye is measured in diopters. For a given person, the focus is modelled by a random variable with normal distribution N(μ, o) with mean μ and standard deviation o. Th focus under which eye correction for nearsightedness (myopia) is considered necessay is -3 diopters. The focus of a normal eye is larger than this value. Mr Y. got arrested for going through a stop sign, not wearing glasses. Throughout the exercise the threshold is set to 5%. Based on 3 measurements on Mr. Y, we have observed an average focus of -0.94. The hypothesis testing the policeman intends to do is H₁: μ> -3. a. Assuming the standard deviation known and equal to o = 1.6 diopters, the rejection region of the test statistics is (-∞, -1.645) O (-1.96, 1.96) * (1.645, ∞)

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The focus of a human eye is measured in diopters. For a given person, the focus is modelled by a random variable with
normal distribution N(μ, o) with mean and standard deviation o. Th focus under which eye correction for
nearsightedness (myopia) is considered necessay is -3 diopters. The focus of a normal eye is larger than this value. Mr
Y. got arrested for going through a stop sign, not wearing glasses. Throughout the exercise the threshold is set to 5%.
Based on 3 measurements on Mr. Y, we have observed an average focus of -0.94. The hypothesis testing the policeman
intends to do is H₁:> -3.
a. Assuming the standard deviation known and equal to o = 1.6 diopters, the rejection region of the test statistics is
(-∞, -1.645)
(-1.96, 1.96) *
(1.645, ∞)
Transcribed Image Text:The focus of a human eye is measured in diopters. For a given person, the focus is modelled by a random variable with normal distribution N(μ, o) with mean and standard deviation o. Th focus under which eye correction for nearsightedness (myopia) is considered necessay is -3 diopters. The focus of a normal eye is larger than this value. Mr Y. got arrested for going through a stop sign, not wearing glasses. Throughout the exercise the threshold is set to 5%. Based on 3 measurements on Mr. Y, we have observed an average focus of -0.94. The hypothesis testing the policeman intends to do is H₁:> -3. a. Assuming the standard deviation known and equal to o = 1.6 diopters, the rejection region of the test statistics is (-∞, -1.645) (-1.96, 1.96) * (1.645, ∞)
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