Question

According to MessageLabs Ltd., 80% of all email sent in July 2010 was spam. A system manager at a large corporation believes that the percentage at his company may be greater than 80%, and he wants to do a hypothesis test to see if there is evidence to support his belief. He examines a random sample of 500 emails received at an email server and finds that 420 of the messages are spam.

1. What is the parameter for this hypothesis test (choose one)?

?μ ?¯y¯ ?p ?̂ p^

2. What is the null hypothesis? ?0H0: ____

   What is the alternative hypothesis? ??HA: ____

3. This test is (Choose one):

   One-sided
   Two-sided

4. What proportion of emails were spam in the sample? Round to two decimal places.

5. Calculate the test statistic. Round to two decimal places.

Answer 1

p : Proportion of spam emails

Claim : greater than 80% of all email sent was spam i.e proporiton of spam emails > 80/100 =0.80 : p >0.80

What is the parameter for this hypothesis test (choose one)?

Population proportion : p

What is the null hypothesis? HO: p = 0.80

What is the alternative hypothesis? HA: p > 0.80

This test is (Choose one):

One-sided

What proportion of emails were spam in the sample?

Number of emails in the sample : n= 500

Number of spam emails : x=420

proportion of emails were spam in the sample: = 420/500 =0.84

What proportion of emails were spam in the sample?

0.84

Calculate the test statistic. Round to two decimal places.

test statistic = 2.24

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For Right tailed test :

p-value = 0.0127