Question

A study surveys students to determine the amount of Facebook use during the time they are doing Math homework. Students are classified into three groups: Non- User, Rarely-Use, Regularly-Use, and their Math scores are recorded. The following data summarize the results.

Facebook Use While Doing Homework
Non-User	Rarely-Use	Regularly-Use
n = 6	n = 8	n = 10	N = 24
M = 6	M = 2	M = 2	G = 72
SS = 30	SS = 33	SS = 42	ΣX2tot = 393

Use an ANOVA with α = .05 to determine whether there are significant differences among the means of the three groups.

A)The alternative hypothesis is:

There are no significant differences in math scores means between the three groups of Facebook users (non-user, rarely-use, regularly use).

There are significant differences in math scores means between the following groups: "non-user" and "rarely-use", and between the following groups: "rarely-use" and "regularly-use"

There are significant differences in math scores means between the following groups: "non-user" and "regularly-use"

There is at least one significant mean difference among the three groups: The math score means of at least two of the groups of Facebook users differ from each other

B)The Critical F-value is:

Note: Leave the two decimal places after the decimal point

C) The F-statistic is:

Note: leave all the decimal places after the decimal point and do not round.

D) Your decision is

Reject the null hypothesis and conclude that there are no significant mean differences among the three groups regarding Math scores

Reject the null hypothesis and conclude that there are significant mean differences among the three groups regarding Math scores

Fail to reject the null hypothesis and conclude that there are no significant mean differences among the three groups regarding Math scores

Fail to reject the null hypothesis and conclude that there are significant mean differences among the three groups regarding Math scores

F) Report the results in APA:

Answer 1

A)The alternative hypothesis is:

There is at least one significant mean difference among the three groups: The math score means of at least two of the groups of Facebook users differ from each other.

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B) Number of treatment, k = 3

Total sample Size, N =24

df(between) = k-1 =2

df(within) = N-k =21

df(total) = N-1 =23

Critical value Fc = F.INV.RT(23.5, 2, 21) = 3.47

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C) SS(Total) = Ʃx² - (Ʃx)²/N = 393 - (72)²/24 = 177

SS(within) =SS1 + SS2 +SS3 = 105

SS(between) = SS(Total) - SS(within) = 72

MS(between) = SS(between)/df(between) =36

MS(within) = SS(within)/df(within) =5

F = MS(between)/MS(within) = 36/5 = 7.2

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D) Your decision is

Reject the null hypothesis and conclude that there are significant mean differences among the three groups regarding Math scores