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Q.4 A researcher is interested in whether people’s level of loneliness would vary as a function of...

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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/ nopetIn a Relationship/ nopetSingle/ havepetIn a Relationship/have pet
Case 18453
Case 27244
Case 38342
Case 46433

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
4.1 Ratings (594 Votes)

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    df MS F    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.
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