Vitamin B6 is one of the vitamins in a multiple vitamin
Chapter 8, Problem 7E(choose chapter or problem)
Vitamin \(\mathrm{B}_{6}\) is one of the vitamins in a multiple vitamin pill manufactured by a pharmaceutical company. The pills are produced with a mean of \(50 \mathrm{mg}\) of vitamin \(\mathrm{B}_{6}\) per pill. The company believes that there is a deterioration of \(1 \mathrm{mg} / \mathrm{month}\), so that after 3 months it expects that \(\mu=47\). A consumer group suspects that \(\mu<47\) after 3 months.
(a) Define a critical region to test \(H_{0}: \mu=47\) against \(H_{1}\): \(\mu<47\) at an \(\alpha=0.05\) significance level based on a random sample of size \(n=20\).
(b) If the 20 pills yielded a mean of \(\bar{x}=46.94\) with a standard deviation of \(s=0.15\), what is your conclusion?
(c) What is the approximate \(p\)-value of this test?
Equation Transcription:
Text Transcription:
B_6
50 mg
1 mg/month
mu=47
mu<47
H_0:=47
H_1;<47
alpha=0.05
n=20
Bar x=46.94
s=0.15
p
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