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 69%. He examines a random sample of 500 emails received at an email server, and finds that 365 of the messages are spam. Can you conclude that greater than 69% of emails are spam? Use both a-0.01 and a = 0.05 levels of significance and the critical value method with the table. Part 1 of 5 State the appropriate null and alternate hypotheses. Ho: P= .69 H1: p> .69 This hypothesis test is a right-tailed V test. Part 2 of 5 Find the critical values. Round the answers to three decimal places. For a=0.01 , the critical value is 2.326 For a-0.05 , the critical value is 1.645 Part: 2/5 Part 3 of 5 Compute the test statistic. Do not round intermediate calculations. Round the answer to two decimal places.

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### Hypothesis Testing for Email Spam Percentage

In this problem, we are given a scenario where a researcher reported that 71.8% of all emails sent in a recent month were spam. A system manager at a large corporation believes that the percentage at his company may be 69%. He examines a random sample of 500 emails received at an email server and finds that 365 of the messages are spam. We are to determine if we can conclude that greater than 69% of the emails are spam using both α = 0.01 and α = 0.05 levels of significance and the critical value method with the table.

### Part 1 of 5
#### State the appropriate null and alternate hypotheses:

\[
H_0: p = 0.69
\]

\[
H_1: p > 0.69
\]

This hypothesis test is a **right-tailed** test.

### Part 2 of 5
#### Find the critical values. Round the answers to three decimal places:

For \( \alpha = 0.01 \), the critical value is \( 2.326 \).

For \( \alpha = 0.05 \), the critical value is \( 1.645 \).

### Part 3 of 5

Compute the test statistic. Do not round intermediate calculations. Round the answer to two decimal places:

\[
z = 
\]
(Note: The image does not provide the value for the test statistic; ensure completion of calculations as needed).
Transcribed Image Text:### Hypothesis Testing for Email Spam Percentage In this problem, we are given a scenario where a researcher reported that 71.8% of all emails sent in a recent month were spam. A system manager at a large corporation believes that the percentage at his company may be 69%. He examines a random sample of 500 emails received at an email server and finds that 365 of the messages are spam. We are to determine if we can conclude that greater than 69% of the emails are spam using both α = 0.01 and α = 0.05 levels of significance and the critical value method with the table. ### Part 1 of 5 #### State the appropriate null and alternate hypotheses: \[ H_0: p = 0.69 \] \[ H_1: p > 0.69 \] This hypothesis test is a **right-tailed** test. ### Part 2 of 5 #### Find the critical values. Round the answers to three decimal places: For \( \alpha = 0.01 \), the critical value is \( 2.326 \). For \( \alpha = 0.05 \), the critical value is \( 1.645 \). ### Part 3 of 5 Compute the test statistic. Do not round intermediate calculations. Round the answer to two decimal places: \[ z = \] (Note: The image does not provide the value for the test statistic; ensure completion of calculations as needed).
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