H₁: P₁ P₂ (b) Determine the type of test statistic to use. Z (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.) -1.645 and 1.645
H₁: P₁ P₂ (b) Determine the type of test statistic to use. Z (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.) -1.645 and 1.645
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![English Air continually monitors the proportion of overweight items checked by passengers on its flights to evaluate the appropriateness of their overweight fees. Recently, a random sample of 258 items checked on English Air flights to North America contained 48 overweight items, and an independent random sample of 235 items checked on English Air flights within Europe contained 26 overweight items.
Based on these samples, can we conclude, at the 0.10 level of significance, that there is a difference between the proportion \( p_1 \) of all items on English Air flights to North America that are overweight and the proportion \( p_2 \) of all items on English Air flights within Europe that are overweight?
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of formulas.)
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[ H_0: p_1 = p_2 \]
\[ H_1: p_1 \neq p_2 \]
(b) Determine the type of test statistic to use.
[Dropdown option labeled "Z" is selected.]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
[An empty box for user input.]
(d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.)
[An empty box for user input.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d0f5607-440e-4fc9-b3b1-9026504c2552%2F14d3d9fe-2ba9-412b-b6c1-332cc37ceb62%2Fow72qvb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:English Air continually monitors the proportion of overweight items checked by passengers on its flights to evaluate the appropriateness of their overweight fees. Recently, a random sample of 258 items checked on English Air flights to North America contained 48 overweight items, and an independent random sample of 235 items checked on English Air flights within Europe contained 26 overweight items.
Based on these samples, can we conclude, at the 0.10 level of significance, that there is a difference between the proportion \( p_1 \) of all items on English Air flights to North America that are overweight and the proportion \( p_2 \) of all items on English Air flights within Europe that are overweight?
Perform a two-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of formulas.)
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[ H_0: p_1 = p_2 \]
\[ H_1: p_1 \neq p_2 \]
(b) Determine the type of test statistic to use.
[Dropdown option labeled "Z" is selected.]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
[An empty box for user input.]
(d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.)
[An empty box for user input.]
![### Hypothesis Testing for Proportions
This exercise guides you through a hypothesis test to compare the proportions of two groups.
#### (a) State the Hypotheses
- **Null Hypothesis (H₀):** \( p_1 = p_2 \)
- **Alternative Hypothesis (H₁):** \( p_1 \neq p_2 \)
#### (b) Determine the Type of Test Statistic
- **Test Statistic:** Z
#### (c) Find the Value of the Test Statistic
- **Input Required:** [Box for calculation input]
#### (d) Critical Values at 0.10 Level of Significance
- **Critical Values:** \(-1.645\) and \(1.645\)
#### (e) Conclusion
- **Question:** Can we conclude that the proportion of items that are overweight is different between the two types of English Air flights?
- **Options:** Yes / No
Use this information to complete the hypothesis test and draw conclusions based on statistical evidence.
#### Additional Tools
- Mathematical symbols and operations are available for detailed statistical calculations.
- Explanation and "Check" buttons provide further guidance and validation of your answers.
#### Note
- This example is taken from a practical exercise aimed at understanding statistical hypothesis testing, particularly focusing on comparing proportions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d0f5607-440e-4fc9-b3b1-9026504c2552%2F14d3d9fe-2ba9-412b-b6c1-332cc37ceb62%2Fd8wnlch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Proportions
This exercise guides you through a hypothesis test to compare the proportions of two groups.
#### (a) State the Hypotheses
- **Null Hypothesis (H₀):** \( p_1 = p_2 \)
- **Alternative Hypothesis (H₁):** \( p_1 \neq p_2 \)
#### (b) Determine the Type of Test Statistic
- **Test Statistic:** Z
#### (c) Find the Value of the Test Statistic
- **Input Required:** [Box for calculation input]
#### (d) Critical Values at 0.10 Level of Significance
- **Critical Values:** \(-1.645\) and \(1.645\)
#### (e) Conclusion
- **Question:** Can we conclude that the proportion of items that are overweight is different between the two types of English Air flights?
- **Options:** Yes / No
Use this information to complete the hypothesis test and draw conclusions based on statistical evidence.
#### Additional Tools
- Mathematical symbols and operations are available for detailed statistical calculations.
- Explanation and "Check" buttons provide further guidance and validation of your answers.
#### Note
- This example is taken from a practical exercise aimed at understanding statistical hypothesis testing, particularly focusing on comparing proportions.
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