A researcher is interested in examining whether the location that a person lives

Question

A researcher is interested in examining whether the location that a person lives is related to the number of hours that they spend on the internet each week. The researcher collected data from a sample of 45 participants who were classified in one of three groups: (1) 15 people who live in an urban setting, (2) 15 people who live in a suburban setting, and (3) 15 people who live in a rural setting. Each participant reported the number of hours they spend on the internet in a typical week (the dependent variable). The researcher found the following descriptive statistics: 1. Urban participants reported an average of 8.9 hours of internet use per week (SD = 2.77) 2. Suburban participants reported an average of 12.7 hours of internet use per week (SD = 4.88) 3. Rural participants reported an average of 9.8 hours of internet use per week (SD = 2.82) The researcher then ran an analysis of variance to determine whether at least two of these means were significantly different. The researcher found the following: 1. Sum of squares between groups = 78.86 2. Sum of squares within groups = 354.51 Use this information answer questions 1 through 5. 1.)What are the degrees of freedom between groups? 2.)What are the degrees of freedom within groups? 3.)What is the mean squares between groups? 4.)What is the mean squares within groups? 5.)What is the obtained F value? 6.)What can the researcher conclude?

Explanation / Answer

1) degrees of freedom between groups =k-1 =3-1=2

2)  degrees of freedom within groups =N-k =45-3 =42

3)  mean squares between groups =SS/dfbw groups =78.86/2=39.43

4) mean squares within groups =SSwithin/dfwithin =354.51/42=8.441

5) obtained F value =mean squares between groups/mean squares within groups =4.6714

6) for 0.05 level and (2,42) df crtiical value of F =3.22

as test statistic is higher than crtiical value therefore we reject null hypothesis.

we have evidence at 0.05 level to conclude that at least two of these means were significantly different.

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