Question

Question 2 (40 pts) For the following data, please answer the following questions Here are the estimated hours spent studying on a typical day of five high school students in each of three types of places: Place of Residence Rural Suburban Urban 3 2 اليا 1 1 0 3 0 4 1 3 5 0 3 1) complete the ANOVA table (30 pts) Sum of square df MSS F P E2 Sum of square Between Within total 2) what is the null hypothesis? (3 pts) 3) based on p, do we reject or not to reject the null hypothesis, and what type of errors incurred? (3 pts) 4) interpreting the cta-square (4 pts) 3

pls show work

Answer 1

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 T_i be the total hours for group i, n_i 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%