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6) A coffee shop claims that their large coffee cups have an average volume of 16 ounces. A random sample of 20 large coffee cups is selected, and their average volume is found to be 15.5 ounces with a sample standard deviation of 0.6 ounces. Is there enough evidence to reject the coffee shop's claim at a significance level of 0.05?

6) A coffee shop claims that their large coffee cups have an average volume of 16 ounces. A random sample of 20 large coffee cups is selected, and their average volume is found to be 15.5 ounces with a sample standard deviation of 0.6 ounces. Is there enough evidence to reject the coffee shop's claim at a significance level of 0.05?

MATLAB: An Introduction with Applications
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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6) A coffee shop claims that their large coffee cups have an average volume of 16 ounces. A random sample of 20 large coffee cups is selected, and their average volume is found to be 15.5 ounces with a sample standard deviation of 0.6 ounces. Is there enough evidence to reject the coffee shop's claim at a significance level of 0.05?
Transcribed Image Text:6) A coffee shop claims that their large coffee cups have an average volume of 16 ounces. A random sample of 20 large coffee cups is selected, and their average volume is found to be 15.5 ounces with a sample standard deviation of 0.6 ounces. Is there enough evidence to reject the coffee shop's claim at a significance level of 0.05?
Expert Solution
Step 1: Basic information

According to the given data:

Population mean open parentheses mu close parentheses space equals space 16 ounces ( volume )

sample size open parentheses n close parentheses space equals space 20

sample mean open parentheses x with bar on top close parentheses space equals space 15.5 ounces ( volume )

sample standard deviation open parentheses s close parentheses space equals space 0.6 ounces ( volume )

Test of given hypothesis:

Null hypothesis open parentheses H subscript 0 close parentheses colon space space mu space equals space 16

Alternative hypothesis open parentheses H subscript 1 close parentheses colon space mu space not equal to space 16

level of significance:  alpha space equals space 0.05`

degree of freedom:  v space equals space n space minus space 1 space equals space 20 space minus space 1 space equals space 19

Table t value:  t subscript open parentheses alpha comma v close parentheses end subscript space equals space t subscript open parentheses 0.05 comma 19 close parentheses space end subscript equals space 2.093   

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