The volume of "one liter" flasks used in laboratories varies about a mean valuethat is controlled by a machine that prints the markings on the flask. Assumethat the volumes of flasks produced by the machine are approximately normallydistributed. A sample of 75 flasks gave a mean volume at the one liter markon the flask of 1.04 liters and a standard deviation of 0.11 liters. Does the datapresent sufficient evidence to conclude that the mean volume at the one litermark is not exactly one liter as claimed by the manufacturer?a) Define the random variable and its assumed probability distribution.b) Test an appropriate set of hypotheses to address the question of interest bycalculating a p-value and interpreting its numerical value in the contextof the problem.c) If your decision in part (b) was an mistake, what type of error did youcommit?

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The volume of "one liter" flasks used in laboratories varies about a mean value
that is controlled by a machine that prints the markings on the flask. Assume
that the volumes of flasks produced by the machine are approximately normally
distributed. A sample of 75 flasks gave a mean volume at the one liter mark
on the flask of 1.04 liters and a standard deviation of 0.11 liters. Does the data
present sufficient evidence to conclude that the mean volume at the one liter
mark is not exactly one liter as claimed by the manufacturer?
a) Define the random variable and its assumed probability distribution.
b) Test an appropriate set of hypotheses to address the question of interest by
calculating a p-value and interpreting its numerical value in the context
of the problem.
c) If your decision in part (b) was an mistake, what type of error did you
commit?

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Step 1

Given Information :

The volume of one liter flasks used in laboratories varies about mean value that is controlled by a machine that prins the markings on the flask . Assume that the volumes of flasks produced by the machine are approximately normally distributed . A sample of 75 flasks gave a mean volume at one liter mark on the flask of 1.04 liters and a standard deviation of 0.11 liters .

Here,

Sample size : n = 75

Sample mean : $\bar{x}$ = 1.04

Sample standard deviation : s = 0.11

State the hypothesis :

H0 : Mean volume at the one liter mark is exactly one liter .

$μ = 1$

H1 : Mean volume at the one liter mark is not exactly one liter .

$μ \neq 1$

A t-test for one mean is a hypothesis test that attempts to make a claim about the population mean ( $σ$ ). This t-test, unlike the z-test, does not need to know the population standard deviation $σ$ .

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