Math  /  Data & Statistics

Question\text{A researcher reported that } 71.8\% \text{ 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 } 77\%. \text{ He examines a random sample of 500 emails received at an email server, and finds that 364 of the messages are spam. Can you conclude that the percentage of emails that are spam differs from } 77\%? \text{ Use both } \alpha=0.01 \text{ and } \alpha=0.05 \text{ levels of significance and the } P\text{-value method with the TI-84 Plus calculator.}
\text{Part 1 of 5}
(a) \text{ State the appropriate null and alternate hypotheses.}
H0:H1:\begin{array}{l} H_{0}: \square^{\otimes} \\ H_{1}: \square^{\otimes} \end{array}
\text{This hypotheses test is a left-tailed} \square \text{ test.}
\text{Correct Answer:}
H0:p=0.77H1:p0.77\begin{array}{l} H_{0}: p=0.77 \\ H_{1}: p \neq 0.77 \end{array}
\text{This hypotheses test is a two-tailed test.}
\text{Part 2 of 5}
(b) \text{ Compute the value of the test statistic. Round the answer to at least two decimal places.}
z=2.23 z=2.23
\text{Correct Answer:}
z=2.23 z=-2.23
\text{Part: } 2/5
\text{Part 3 of 5}
(c) \text{ Compute the } P\text{-value. Round the answer to at least four decimal places,}
P-value = P \text{-value }=

Studdy Solution
Draw a conclusion based on the P-value:
At α=0.01 \alpha = 0.01 , we fail to reject the null hypothesis. There is not enough evidence to conclude that the percentage of spam emails differs from 77%.
At α=0.05 \alpha = 0.05 , we reject the null hypothesis. There is enough evidence to conclude that the percentage of spam emails differs from 77%.

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