Hypothesis tests for two means, F-test for two Variances, Hypothesis tests for paired data

Question 1

What is the difference between independent and dependent samples and how can this be determined?

Answer 1

• Independent
  
  • Our two samples are not related; samples drawn randomly from different populations
• Dependent
  
  • Also called paired; used when samples are linked in some way - two questions asked of same person; two sunscreens, one tested on each arm etc;
  • check by jumbling up order and seeing if it still makes sense e.g. before and after weights

Question 2

What is the F distribution?

Answer 2

• Do not interpolate, use closest
• Only exists for values > 0, only supports positive domain
• Positively skewed
• Peak of 1
• Tables (pages) give upper cut off point of distribution (α value)
• Can only get one tail as not symmetric
• Only look at upper tail (α/2) and create t.s as bigger than 1 so can be compared - test is 2 tailed though
• F - Distribution: requires two degrees of freedom

Question 3

What is true of the F Test?

Answer 3

F-test requires that both populations are normally distributed. This is NOT a CLT assumption!

Question 4

How is the test for difference in means done for paired samples?

Answer 4

• For each observation, calculate Xd = X1 - X2

- Then calculate X̅d and sd (mean and standard deviation of differences)

Question 5

What is true of testing the difference between two proportions?

Answer 5

• Our samples MUST be independent