Question

Assume that a new professional coffee maker sales representative claims that the new coffee maker will increase coffee made by at least 30 cups per hour. A coffee shop chain manager buys the new machine for his 15 coffee shop branches in Dubai and finds that the average increase was 32 cups. Assume that the standard deviation is 7 cups for this coffee maker.

1. State the null and alternative hypotheses.

2. Test the hypotheses at the 5% significance level. What is the p-value of the test?

3. What is your conclusion in the context of the question?

4. Interpret the p-value you found above.

5. What type of error you can commit here? Explain in the context of the question. Also, what are the

   implications of this error?

Answer 1

Ho :   µ =   30                  
Ha :   µ >   30       (Right tail test)          
                          
Level of Significance ,    α =    0.05                  
population std dev ,    σ =    7.0000                  
Sample Size ,   n =    15                  
Sample Mean,    x̅ =   32.0000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   7.0000   / √    15   =   1.8074      
Z-test statistic= (x̅ - µ )/SE = (   32.000   -   30   ) /    1.8074   =   1.11
                             
                          
p-Value   =   0.1342   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value>α, Do not reject null hypothesis           

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p value is probability of null hypothesis being true

that is, there is a probability of 0.1342 that null hypothesis is true

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type II error can be commeited here

type II error is non rejection of false null hypothesis

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consequences are that we concluded that mean number of cups are not greater than 30 but in actual they are greater than 30

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thanks

revert back for doubt

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