1)
Sum of square | Sum of square | df | MSS | F | P | E2 |
Between | 10 | 2 | 5 | 2.5 | 0.1237 | 0.2941 |
Within | 24 | 12 | 2 | |||
Total | 34 | 14 |
Degree of freedom of Between, df Between = Number of level - 1 = 3 - 1 = 2
Degree of freedom of Within, df Within = Number of observations - Number of level = 5 * 3 - 3 = 12
Degree of freedom of Total = Number of observations - 1 = 5 * 3 - 1 = 14
Let Ti be the total hours for group i, ni be number of observations of group i.
Let G be the total hours of all observations and N be total number of observations.
ΣX2 is sum of squares of all obsrvations.
T1 = 5, T2 = 15 , T3 = 10
G = 5 + 15 + 10 = 30
ΣX2 = 11 + 53 + 30 = 94
SST = ΣX2 - G2/N = 94 - 30^2/15 = 34
SS Between = ΣT2/n - G2/N = (5^2 /5 + 15^2 /5 + 10^2 /5 ) - 30^2/15 = 10
SS Within = 34 - 10 = 24
MSS = SS / df
F = MSS Between / MSS Within = 5/2 = 2.5
P-value = P(F > 2.5, 2, 12) = 0.1237
Eta Squared = SS Between / SS Total = 10 / 34 = 0.2941
2)
Null Hypothesis H0: The mean number of hours spent by high school students is each of the three type of places are equal.
3)
Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that to reject the claim that the mean number of hours spent by high school students is each of the three type of places are equal.
As, we fail to reject null hypothesis H0, we may commit Type II error in case the null hypothesis is false.
4)
The percentage of variation in number of hours spent by high school students explained by the type of places is 29.41%
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