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A professional employee in a large corporation receives an average of

`\mu =41.7`

e-mails per day. An anti-spam protection program was installed in the company's server and one month later a random sample of 45 employees showed that they were receiving an average of

`\bar{x} =`

36.2 e-mails per day. Assume that

`\sigma =18.45`

. Use a

`5%`

level of significance to test whether there has been a change (either way) in the average number of emails received per day per employee. a.) What is

`a`

? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

`\alpha =`

`◻`

`H_(0):\mu =`

`◻`

`H_(1):\mu `

`◻`

The test is a

`◻`

Select an answer test b.) Identify the Sampling Distribution you will use. What is the value of the test statistic? The best sampling distribution to use is the

`◻`

distribution. The test statistic (

`z`

or

`t`

value) is

`=`

`◻`

c.) Find or estimate the

`P`

-value for the test. The

`p`

-value is

`=`

`◻`

d.) Conclude the test. Based on this we will Select an answer the null hypothesis.