Vitamin B6 is one of the vitamins in a multiple vitamin pill manufactured by a phar- maceutical company. The pills are produced with a mean of 50 mg of vitamin B6 per pill. The company believes that there is a deterioration of 1 mg/month, so that after 4 months it expects that μ 46. A consumer group suspects that < 46 after 4 months. Assume the amount of vitamin B6 per pill is normally distributed with unknown variance. = (i) Define a test for Ho = 46 against H₁ μ< 46 at a significance level a = 0.01 based on a random sample of size n. (ii) If a sample of 20 pills yielded a mean of x = 45.88 with a (sample) standard deviation of s = 0.17, what is the conclusion based on your test defined in part (i)? Also, compute the associated p-value. (iii) Find the smallest significance level a under which we can reject Ho based on the data given in part (ii). Does it equal to the p-value found in part (ii)? Explain why.
Vitamin B6 is one of the vitamins in a multiple vitamin pill manufactured by a phar- maceutical company. The pills are produced with a mean of 50 mg of vitamin B6 per pill. The company believes that there is a deterioration of 1 mg/month, so that after 4 months it expects that μ 46. A consumer group suspects that < 46 after 4 months. Assume the amount of vitamin B6 per pill is normally distributed with unknown variance. = (i) Define a test for Ho = 46 against H₁ μ< 46 at a significance level a = 0.01 based on a random sample of size n. (ii) If a sample of 20 pills yielded a mean of x = 45.88 with a (sample) standard deviation of s = 0.17, what is the conclusion based on your test defined in part (i)? Also, compute the associated p-value. (iii) Find the smallest significance level a under which we can reject Ho based on the data given in part (ii). Does it equal to the p-value found in part (ii)? Explain why.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:Vitamin B6 is one of the vitamins in a multiple vitamin pill manufactured by a phar-
maceutical company. The pills are produced with a mean of 50 mg of vitamin B6 per pill.
The company believes that there is a deterioration of 1 mg/month, so that after 4 months
it expects that µ = 46. A consumer group suspects that < 46 after 4 months. Assume the
amount of vitamin B6 per pill is normally distributed with unknown variance.
: µ
(i) Define a test for Ho = 46 against H₁ μ< 46 at a significance level a = 0.01 based
: µ
on a random sample of size n.
(ii) If a sample of 20 pills yielded a mean of x = 45.88 with a (sample) standard deviation of
s = 0.17, what is the conclusion based on your test defined in part (i)? Also, compute
the associated p-value.
(iii) Find the smallest significance level a under which we can reject Ho based on the data
given in part (ii). Does it equal to the p-value found in part (ii)? Explain why.
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