Q1) Stockbroker at Critical Securities reported that mean rate of return on a sample of 10 oil stocks was 12.6 percent with the standard deviation of 3.9%. Mean rate of return on a sample of 8 utility stocks was 10.9% with standard deviation of 3.5%. At 0.05 significance level, can we conclude that there is more variation in oil stocks?

2) Following hypotheses are given,

            H₀: s₁² ≤ s₂²   

            H₁: s₁² > s₂²

Random sample of five observations from first population resulted in standard deviation of 12. A random sample of 7 observations from second population illustrated a standard deviation of 7. At 0.01 significance level, is there more variation in first population?

Q3) Research at University of Toledo indicates that 50% of students change their major area of study after their first year in the program. A random sample of 100 students in college of Business disclosed that 48 had changed their major area of study after their first year of program. Has there been a noteworthy decrease in proportion of students who change their major after first year in this program? Test at 0.05 level of significance.