Question

spam: a researcher reported that 71.8% of all email sent in a recent month was spam. a system manager at a large corporation believes that the percentage at his company may be 71%. he examines a random sample of 500 emails received at an email server, and finds that 380 of the messages are spam. can you conclude that the percentage of emails that are spam differs from 71%? use both \\(\alpha = 0.10\\) and \\(\alpha = 0.01\\) levels of significance and the p - value method and excel.\
part: 0 / 5\
part 1 of 5\
(a) state the appropriate null and alternate hypotheses.\
\\(h_0:\\) \\(\square\\)\
\\(h_1:\\) \\(\square\\)\
this hypothesis test is a \\(\boldsymbol{\text{select } \gt}\\) test.\
\\(\boldsymbol{\text{right - tailed}}\\) \\(\boldsymbol{\text{left - tailed}}\\) \\(\boldsymbol{\text{two - tailed}}\\)\
\\(\boldsymbol{\text{\\(\
eq\\)}}\\) \\(\boldsymbol{\text{\\(\lt\\)}}\\) \\(\boldsymbol{\text{\\(\gt\\)}}\\) \\(\boldsymbol{\text{\\(=\\)}}\\) \\(p\\)

Explanation:

Step1: Define Null Hypothesis

The null hypothesis (\(H_0\)) is a statement of no difference or the status quo. Here, the system manager believes the percentage at his company may be 71%, so we test if the proportion \(p\) (percentage of spam emails) is equal to 71% or 0.71. Thus, \(H_0: p = 0.71\).

Step2: Define Alternative Hypothesis

The researcher wants to test if the percentage differs from 71%, so the alternative hypothesis (\(H_1\)) is that the proportion \(p\) is not equal to 0.71. Thus, \(H_1: p
eq 0.71\). Also, since we are testing for a difference (not greater or less), this is a two - tailed test.

Answer:

\(H_0: p = 0.71\), \(H_1: p
eq0.71\), and the test is two - tailed.