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-0.0 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. -.69 H: 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 3 of 5 Compute the test statistic. Do not round intermediate calculations. Round the answer to decimal places. 1.93 Part 4 of 5 Determine whether to reject H At the a– 0.01 level, do not reject v the null hypothesis Ho. At the a=0.05 level, reject ▼ the null hypothesis Ho. Part: 4 / 5 Part 5 of 5 State a conclusion. At the a- 0.01 level of significance, there (Choose one) V enough evidence to conclude that greater than 69% of emails are spam. At the a-0.05 level of significance, there (Choose one) ▼ enough evidence to conclude that greater than 69% of emails are spam.
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-0.0 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. -.69 H: 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 3 of 5 Compute the test statistic. Do not round intermediate calculations. Round the answer to decimal places. 1.93 Part 4 of 5 Determine whether to reject H At the a– 0.01 level, do not reject v the null hypothesis Ho. At the a=0.05 level, reject ▼ the null hypothesis Ho. Part: 4 / 5 Part 5 of 5 State a conclusion. At the a- 0.01 level of significance, there (Choose one) V enough evidence to conclude that greater than 69% of emails are spam. At the a-0.05 level of significance, there (Choose one) ▼ enough evidence to conclude that greater than 69% of emails are spam.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Topic Video
Question
![### Spam Email Analysis
#### Problem Statement
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. Can you conclude that greater than 69% of emails are spam? Use 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.**
Null Hypothesis \( H_0 \):
\[ p = 0.69 \]
Alternate Hypothesis \( H_1 \):
\[ p > 0.69 \]
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.**
Calculated test statistic \( z \):
\[ z = 1.93 \]
### Part 4 of 5
**Determine whether to reject \( H_0 \).**
At the \( \alpha = 0.01 \) level,
\[ \text{do not reject} \]
the null hypothesis \( H_0 \).
At the \( \alpha = 0.05 \) level,
\[ \text{reject} \]
the null hypothesis \( H_0 \).
### Part 5 of 5
**State a conclusion.**
At the \( \alpha = 0.01 \) level of significance, there is
\[ \text{not enough} \]
evidence to conclude that greater than 69% of emails are spam.
At the \( \alpha = 0.05 \) level of significance, there is
\[ \text{enough} \]
evidence to conclude that greater than 69% of emails are spam.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa666cb21-4e01-4a08-9d64-d66a4b2c67e7%2F1a43d6a5-1c2d-4a63-ba73-9a6c797208f7%2F0ruzy4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Spam Email Analysis
#### Problem Statement
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. Can you conclude that greater than 69% of emails are spam? Use 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.**
Null Hypothesis \( H_0 \):
\[ p = 0.69 \]
Alternate Hypothesis \( H_1 \):
\[ p > 0.69 \]
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.**
Calculated test statistic \( z \):
\[ z = 1.93 \]
### Part 4 of 5
**Determine whether to reject \( H_0 \).**
At the \( \alpha = 0.01 \) level,
\[ \text{do not reject} \]
the null hypothesis \( H_0 \).
At the \( \alpha = 0.05 \) level,
\[ \text{reject} \]
the null hypothesis \( H_0 \).
### Part 5 of 5
**State a conclusion.**
At the \( \alpha = 0.01 \) level of significance, there is
\[ \text{not enough} \]
evidence to conclude that greater than 69% of emails are spam.
At the \( \alpha = 0.05 \) level of significance, there is
\[ \text{enough} \]
evidence to conclude that greater than 69% of emails are spam.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman