Q.4 A researcher is interested in whether people’s level of loneliness would vary as a function of...
Free
70.2K
Verified Solution
Link Copied!
Question
Statistics
Q.4 Aresearcher is interested in whether people’s level of lonelinesswould vary as a function of their relationship status (single vs.in a relationship), and how such difference might depend on whetherpeople own a pet or not. She recruited a group of participants,asking them about their relationship status, pet ownership, and theperceived level of loneliness. The data are as below, with a highernumber denoting greater level of loneliness:
Single/ nopet In a Relationship/ nopet Single/ havepet In a Relationship/have pet Case 1 8 4 5 3 Case 2 7 2 4 4 Case 3 8 3 4 2 Case 4 6 4 3 3
Conduct a properstatistical test by hand calculation to test the hypotheses in b.,with 5% as the level of significance (α). (For this exercise, thedata assumptions of your chosen statistical test can be taken asreasonably met.) Show your calculation formulae and steps. In caseyou decide to conduct an ANOVA, you are not required to conduct anypost-hoc comparisons. Decide whether to reject the null hypothesisor not for each effect and state the basis of your decision.
*Sorry, reuploaded thequestion because I wrote the wrong numbers
Q.4 Aresearcher is interested in whether people’s level of lonelinesswould vary as a function of their relationship status (single vs.in a relationship), and how such difference might depend on whetherpeople own a pet or not. She recruited a group of participants,asking them about their relationship status, pet ownership, and theperceived level of loneliness. The data are as below, with a highernumber denoting greater level of loneliness:
| Single/ nopet | In a Relationship/ nopet | Single/ havepet | In a Relationship/have pet | |
| Case 1 | 8 | 4 | 5 | 3 |
| Case 2 | 7 | 2 | 4 | 4 |
| Case 3 | 8 | 3 | 4 | 2 |
| Case 4 | 6 | 4 | 3 | 3 |
Conduct a properstatistical test by hand calculation to test the hypotheses in b.,with 5% as the level of significance (α). (For this exercise, thedata assumptions of your chosen statistical test can be taken asreasonably met.) Show your calculation formulae and steps. In caseyou decide to conduct an ANOVA, you are not required to conduct anypost-hoc comparisons. Decide whether to reject the null hypothesisor not for each effect and state the basis of your decision.
*Sorry, reuploaded thequestion because I wrote the wrong numbers
Answer & Explanation Solved by verified expert
This is One-Way ANOVA analysis because we have two variables, namely, relationship status and whether people own a pet or not.
The hypothesis being tested is:
H0: µ1 = µ2 = µ3 = µ4
Ha: At least one means is not equal for all groups
The output is:
| Mean | n | Std. Dev | |||
| 7.3 | 4 | 0.96 | Group 1 | ||
| 3.3 | 4 | 0.96 | Group 2 | ||
| 4.0 | 4 | 0.82 | Group 3 | ||
| 3.0 | 4 | 0.82 | Group 4 | ||
| 4.4 | 16 | 1.93 | Total | ||
| ANOVA table | |||||
| Source | SS | Â Â df | MS | F | Â Â p-value |
| Treatment | 46.25 | 3 | 15.417 | 19.47 | .0001 |
| Error | 9.50 | 12 | 0.792 | ||
| Total | 55.75 | 15 |
Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we can conclude that at least one group of relationship status has a significant difference mean of the level of loneliness from the other 3 groups.
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
- Unlimited Question Access with detailed Answers
- Zin AI - 3 Million Words
- 10 Dall-E 3 Images
- 20 Plot Generations
- Conversation with Dialogue Memory
- No Ads, Ever!
- Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Other questions asked by students
StudyZin's Question Purchase
1 Answer
$0.99
(Save $1 )
One time Pay
- No Ads
- Answer to 1 Question
- Get free Zin AI - 50 Thousand Words per Month
Unlimited
$4.99*
(Save $5 )
Billed Monthly
- No Ads
- Answers to Unlimited Questions
- Get free Zin AI - 3 Million Words per Month
*First month only
Free
$0
- Get this answer for free!
- Sign up now to unlock the answer instantly
You can see the logs in the Dashboard.