Probability and Statistical Inference (9th Edition)
Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Chapter 8.1, Problem 7E

Vitamin B6 is one of the vitamins in a multiple vitamin pill manufactured by a pharmaceutical 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 three months it expects that μ = 47 .

A consumer group suspects that μ < 47 after three months.

(a) Define a critical region to test H 0 : μ = 47 against H 1 : μ < 47 at an α = 0.05 significance level based on a random sample of size n = 20 .

(b) If the 20 pills yielded a mean of 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?

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