Sandra's marketing firm is advertising a new type of coffee for their client. As part of their market research, the firm randomly selects 40 adults from the tri-state area and ask them how much they spend annually on coffee. The sample mean is $178 and the sample standard deviation is $14. Based on this data, the manager of the firm claims that he believes the average annual amount spent on coffee by all adults in the tri-state area is less than $185. Is the manager correct? Test his claim at the 0.01 significance level.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Sandra's marketing firm is advertising a new type of coffee for their client. As part of their market research, the firm randomly selects 40 adults from the tri-state area and ask them how much they spend annually on coffee. The sample mean is $178 and the sample standard deviation is $14. Based on this data, the manager of the firm claims that he believes the average annual amount spent on coffee by all adults in the tri-state area is less than $185. Is the manager correct? Test his claim at the 0.01 significance level. 

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Step 1

The summary of the statistics is,

Statistics homework question answer, step 1, image 1

The type of test is left tailed test

Step 2

The value of test statistic is,

Statistics homework question answer, step 2, image 1

The degree of freedom is,

df=n-1   =40-1   =39

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