Spam is of concem to anyone with an email address Several co

Spam is of concem to anyone with an e-mail address. Several companies offer protection by eliminating spam e-mail as soon as they hit an inbox. State your hypotheses Which hypothesis test should you use? State your rejection rule (use the p-value approach). Show how the test statistic was calculated (write down the formula and plug in the numbers.) What is the p-value? State your conclusion.

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.02
Ha:   p   >   0.02

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b)

We should use a z test for population proportion.

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c)

As this is a 0.10 level, right tailed test, then by table/technology,

Reject Ho when z > 1.281551566. [ANSWER]

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d)

As we see, the hypothesized po =   0.02      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.040106952      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.007239228      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.777499592   [ANSWER]

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e)  
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.002738945   [ANSWER]

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f)

As z > 1.281, and P < 0.1, we Reject Ho.

There is significant evidence that the proportion of spam getting through is greater than 2% at 0.1 level. [CONCLUSION]