Question

Explore the Data and Set up the Test: The data is from current ST314 students. The variables are hours spent playing video games (all types) and the student's current major. average number of hours playing video games between majors for ST314 students Mecht E or Other mean SD n 8 10 43 CS 7 9 14 MechE IE or Other CS Civil or CEM CM or CEM o 13 18 35 3 3 5 15 20 40 60 80 hours per week gaming a. (1 point) From the side-by-side box plot, does there look to be a difference between the averages? Explain whether there is visual evidence of a significant different. b. (0.5 points) State the appropriate null and alternative hypothesis for the Single Factor ANOVA F test. c. (2 points) State the conditions for the Single Factor ANOVA F Test. Is it reasonable to seem that these conditions are satisfied? If not, still proceed.

Answer 1

Solution: We know that the data is about the hours spent by the students of various streams

The given is boxplot and measure of central tendancy and varience as well

a) In the side by side box plot we can see the quartiles and the max and min observation and the outliers as well.

We can see that the median i.e second quartile the average are not same since the middle most lines are different for different box plot

From the values of mean also we can say that there is difference among the averages.But in case of mechanical and IE students there is no much difference in the averages.

b) The hypothesis for the single factor ANOVA is as follows

H0: Treatments are not significantly different

vs H1: Treatments are significantly different or at least one is significant

In this case, Ho: The average hours spent by the students are not significatly different

vs H1: The average hours spent by the students are significatly different or average of hours of at least one stream students is different

c) The assumptions that need to be satisfied for single factor ANOVA are as follows

i) The data should be normally distributed

ii) The error term should follow the standard normal distribution.

iii) The sum of errors should be zero.

These assumption are necessary. In the given boxplots we can see that there are outliers present in the data.They can violate the assumption about the residuals. Thus we need to remove them  

d) In the given figure we can see that the ANOVA is given.

The MStr gives between the group variablity and the MSE gives the within the group variability.

Here from the table

MStr =402.1

MSE=  161.3

e) Now in the table its given that the F statistic is 2.493 and the corresponding p value is 0.0642

The test statistic F = MStr / MSE

= 2.493

We have to check for the significance at 10% los for the average difference between the treatment

The p value is 0.0642 < alpha =0.10

Thus we reject H0

Hence, The Treatments are significantly different i.e The average hours spent by at least one group of the students is significatly different.

Here p value and alpha value are not far away. there is no strong difference between them. Thus we can strongly comment for rejection of H0.

f) The given table is for tuckey test for multiple comparison

We know that at least one treatment is significant and we want to comapre all the treatments by pairs.

by performing tuckyes test we get result as given

We check for the p values to see if difference between  pair of treatment is significant

The list of not significant treatments or group of students

IE- civil

mech - civil

IE - CS

mech - IE

Since for all these pair groupsp value is greater than 0.10

and the significant one is CS - civel group

The 90% CI for the one with lowest p value is (0.9622204 , 19.152065)

This confidence interval includes the difference between the average hours of playing games of CS and Civil groups.The difference between them is of 10.0517 hours. The 90% CI gives the interval such that 90% confidently we can say that the difference value will lie in it.