Question

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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 68%. He examines a random sample of 500 emails received at an email server, and finds that 361 of the messages are spam. Can you conclude that greater than 68% of emails are spam? Use both q=0.10 and a-0.01 levels of significance and the critical value method with the table.

Answer 1

Sol:

1).

a).

null Hypothesis:               Ho:	p	=	0.680
alternate Hypothesis:    Ha:	p	<	0.680

, left tailed

b).

Standard Error= square root of(p*(1-p)/n)

= Square root of(0.68*(1-0.68)/500

=0.0208

Sample Proportion(p^) = x/n

= 361/500

= 0.722

test statistic z = p^-p/Se

= (0.722-0.68)/0.0208

= 2.019.

we can conclude that less than 78% of emails are spam , as test statistic is lower than critical value -1.28

we can conclude that less than 78% of emails are spam,as test statistic is lower than critical value -1.28

2).

The Null Hypothesis is

H0 = $\mu$ 0 = 35000.

The Alternative Hypothesis

H1 = $\mu$ : $\neq$ 35000.

This Hypothesis is a Right tailed test

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