In single-factor ANOVA with I treatments and J observationsper treatment, let m 5 (1yI)omi.a. Express E(X..) in terms of m. [Hint: X.. 5 (1yI)oXi?]b. Determine E(Xi?2). [Hint: For any rv Y, E(Y2) 5V(Y) 1 [E(Y)]2.]c. Determine E(X..2 ).d. Determine E(SSTr) and then show thatE(MSTr) 5 s2 1JI 2 1o(mi 2 m)2e. Using the result of part (d), what is E(MSTr) whenH0 is true? When H0 is false, how does E(MSTr)compare to s2?

Week 2: Lecture 3 ● Spread: How much the data values vary around each other. ○ Range: How far apart are the two extremes. Also, sensitive to outliers. (e.g. range= max-min) ● Interquartile Range: the value that is just above the lower 25% of the data values, namely Q 1 ○ Range of middle half of the data ■ IQR = Q - Q *IQR is like median, not affected by outliers or 3 1 skewness of distribution ● Upper Quartile (3rd Quartile): the value that is just above the lower 75% of data values, namely Q 3 ■ E.g. 150 150 152 154 156 I 156 157 157 158 159. Answer: Q =152, Q =157 1 3 ● Standard deviation: measures how far the data values are f