At a nearby college, there is a school-sponsored website that matches people looking for roommates. According ta the school's reports, 43% af students will find a match their first time using the site. A writer for the school newspaper tests this claim by choosing a random sample aof 170 students who visited the site looking for a roommate. Of the students surveyed, 58 said they found a match their first time using the site. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level af significance, to reject the ciaim that the proportion, P, of all students who will find a match their first time using the site is 43%. (a) State the null hypothesis A and the alternative hypothesis H that you wauld use for the test. H 0 (b) For your hypothesis test, you will use a Z-test. Find the values of P and n(1-p) to confirm that a Z-test can be used. (One standard is that p2 10 and 4(1-9)2 10 under the assumption that the null hypothesis is true.) Here is the sample size and P is the papulation proportion you are testing. (1-7) =0 (c) Perform a Z-test. Here is some information to help you with your Z-test. • F0.as is the value that cuts off an area of 0.05 in the right tail of the distribution. • The value of the test statistic is given by = Standard Normal Distribution Step 1: Seect one-taiked or two-lailed. O One-taiked O Two-lalud Stap 2: Enter the critical valau(s). (Round to 3 decimal places.) Stap 3: Enter the test statistic. (ound to 3 decimal places.) 8 會 回
At a nearby college, there is a school-sponsored website that matches people looking for roommates. According ta the school's reports, 43% af students will find a match their first time using the site. A writer for the school newspaper tests this claim by choosing a random sample aof 170 students who visited the site looking for a roommate. Of the students surveyed, 58 said they found a match their first time using the site. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level af significance, to reject the ciaim that the proportion, P, of all students who will find a match their first time using the site is 43%. (a) State the null hypothesis A and the alternative hypothesis H that you wauld use for the test. H 0 (b) For your hypothesis test, you will use a Z-test. Find the values of P and n(1-p) to confirm that a Z-test can be used. (One standard is that p2 10 and 4(1-9)2 10 under the assumption that the null hypothesis is true.) Here is the sample size and P is the papulation proportion you are testing. (1-7) =0 (c) Perform a Z-test. Here is some information to help you with your Z-test. • F0.as is the value that cuts off an area of 0.05 in the right tail of the distribution. • The value of the test statistic is given by = Standard Normal Distribution Step 1: Seect one-taiked or two-lailed. O One-taiked O Two-lalud Stap 2: Enter the critical valau(s). (Round to 3 decimal places.) Stap 3: Enter the test statistic. (ound to 3 decimal places.) 8 會 回
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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![### Hypothesis Testing for Roommate Matching Success
**Background:**
A school's report claims that 43% of students will find a match their first time using a school-sponsored roommate matching website. A study surveyed 170 students, and 58 found a match on their first try. A hypothesis test will determine if there is sufficient evidence to reject or support the school's claim at a 0.10 level of significance.
**Steps to Conduct the Hypothesis Test:**
**(a) State the Hypotheses:**
- **Null Hypothesis (H₀):** The population proportion, \( p \), is 43% (0.43).
- **Alternative Hypothesis (H₁):** The population proportion \( p \) is not 43% (0.43).
**(b) Conditions for Z-Test:**
A Z-test is appropriate if:
- \( np \geq 10 \) and \( n(1-p) \geq 10 \).
Here, \( n \) is the sample size (170), and \( p \) is the population proportion (0.43).
**(c) Perform the Z-Test:**
**Z-Statistic Calculation:**
- The Z-statistic is calculated using:
\[
z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}
\]
Here, \( \hat{p} \) is the sample proportion, calculated as \(\frac{58}{170}\).
**Distribution Information:**
- A standard normal distribution curve with marked regions for rejection based on \(\alpha = 0.10\) (significance level).
**(d) Conclusion:**
Based on the test statistic's position in relation to the rejection region:
- **If Z lies in the rejection region:** The null hypothesis is rejected, indicating sufficient evidence to reject the claim that 43% of students will find a match.
- **If Z does not lie in the rejection region:** The null hypothesis is not rejected, suggesting insufficient evidence to reject the claim.
**Graphical Representation:**
- **Standard Normal Distribution Curve:**
- Displays a bell-shaped curve.
- Areas under the curve correspond to probabilities.
- Shaded regions represent areas beyond the critical value (for \(\alpha = 0.10\)), indicating rejection regions for the hypothesis test.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbce1f951-db00-41fc-b226-5b8bf4ea58a6%2Fd35c36b7-0ce2-4962-a402-8fb567a7cde4%2F75qmon9_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Roommate Matching Success
**Background:**
A school's report claims that 43% of students will find a match their first time using a school-sponsored roommate matching website. A study surveyed 170 students, and 58 found a match on their first try. A hypothesis test will determine if there is sufficient evidence to reject or support the school's claim at a 0.10 level of significance.
**Steps to Conduct the Hypothesis Test:**
**(a) State the Hypotheses:**
- **Null Hypothesis (H₀):** The population proportion, \( p \), is 43% (0.43).
- **Alternative Hypothesis (H₁):** The population proportion \( p \) is not 43% (0.43).
**(b) Conditions for Z-Test:**
A Z-test is appropriate if:
- \( np \geq 10 \) and \( n(1-p) \geq 10 \).
Here, \( n \) is the sample size (170), and \( p \) is the population proportion (0.43).
**(c) Perform the Z-Test:**
**Z-Statistic Calculation:**
- The Z-statistic is calculated using:
\[
z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}
\]
Here, \( \hat{p} \) is the sample proportion, calculated as \(\frac{58}{170}\).
**Distribution Information:**
- A standard normal distribution curve with marked regions for rejection based on \(\alpha = 0.10\) (significance level).
**(d) Conclusion:**
Based on the test statistic's position in relation to the rejection region:
- **If Z lies in the rejection region:** The null hypothesis is rejected, indicating sufficient evidence to reject the claim that 43% of students will find a match.
- **If Z does not lie in the rejection region:** The null hypothesis is not rejected, suggesting insufficient evidence to reject the claim.
**Graphical Representation:**
- **Standard Normal Distribution Curve:**
- Displays a bell-shaped curve.
- Areas under the curve correspond to probabilities.
- Shaded regions represent areas beyond the critical value (for \(\alpha = 0.10\)), indicating rejection regions for the hypothesis test.
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