Exam 3 (Chapters 9-11)

Question 1

null and alternative hypotheses

Answer 1

the null hypothesis is always that there is no difference: H0: M = μ or M-μ = 0. alternative hypothesis: HI: M>μ or M-μ>0 (significantly greater) or M<μ or M-μ<0 (less significant)

Question 2

when to use each statistical test

Answer 2

• z-test: larger sample, the population standard deviation σ is known, you can assume the distribution is normal
• t-test: smaller samples, population standard deviation is unknown
• independent t-test: the groups are independent of one another (e.g., class A vs class B or men vs women)
• paired t-test: the groups are dependent (e.g., comparing student’s test scores before and after intervention or comparing two different methods on the same participants).

Question 3

how to determine significance using a z-score

Answer 3

• find the z-score: z=(M-μ )/SEM
• to get the SEM: σ/√n and you also need M
• you then need to compare that z-score to the critical Z from the unit normal table (Z-table) for alpha = 0.01 tailed

Question 4

one tailed test vs two tailed t-test

Answer 4

• one-tailed: use when you are testing for a significant difference in one direction only. (i.e., greater or less)
• two-tailed: use when testing for significance in either direction

Question 5

determining significance using a t-test

Answer 5

• t = M - μ) / Sm (same as z-score, but we have estimated standard error (Sm).
• so you need Sm (Sm = √S2/n) which means you have to find the sample variance S2 (SS/(n-1))
• SS = Σ(X - M)2 or ΣX2-(ΣX)2/n
• the t score must be compared to the critical t-stat for alpha = 0.001 tailed with the right df (degrees of freedom) - not the same as critical Z df = n-1

Question 6

confidence intervals

Answer 6

confidence intervals come from the mean +- CRITICAL T (the one giving you the desired confidence, comes from the table) times the estimated standard error