Question

Spam is of concern to anyone with an e-mail address. Several companies offer protection by eliminating spam e-mails as soon as they hit an inbox. To examine one such product, a manager randomly sampled his daily emails for 50 days after installing spam software. A total of 374 e-mails were received, of which 15 were spam. Is there evidence that the proportion of spam getting through is greater than 2%? α = 0.10 a. State your hypotheses. b. Which hypothesis test should you use? c. State your rejection rule (use the p-value approach). d. Show how the test statistic was calculated (write down the formula and plug in the numbers). e. What is the p-value? f. State your conclusion.

Answer 1

Ho :   p =    0.02                  
H1 :   p >   0.02       (Right tail test)          
                          
Level of Significance,   α =    0.10                  
Number of Items of Interest,   x =   15                  
Sample Size,   n =    374                  
                          
Sample Proportion ,    p̂ = x/n =    0.0401                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0072                  
Z Test Statistic = ( p̂-p)/SE = (   0.0401   -   0.02   ) /   0.0072   =   2.7775
                          

                          
p-Value   =   0.0027 [Excel function =NORMSDIST(-z)      

Decision:   p-value<α , reject null hypothesis          

           
There is enough evidence to say taht  proportion of spam getting through is greater than 2%

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THANKS

revert back for doubt

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