BUSS1020 Chapter Notes - Chapter 10: Confidence Interval, Null Hypothesis, Alternative Hypothesis
28 May 2018
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CHAPTER 10: FUNDAMENTALS OF HYPOTHESIS TESTING – TWO-SAMPLE TESTS
COMPARING THE MEANS OF TWO INDEPENDENT POPULATIONS
• Difference between two means if σ unknown:
o Assumptions:
§ Samples are randomly and independently drawn
§ Pop is normally distributed or sample sizes are large enough
for CLT to hold
o Null hypothesis: H0: µ1 - µ2 = 0
o Alternative hypothesis: H1: µ1 - µ2 ≠ 0
o σ1 and σ2 assumed equal:
§ Use pooled variance to estimate unknown σ
§
§ Confidence Interval:
o σ1 and σ2 assumed unequal:
§
§ With degree of freedom, v:
§ Confidence Interval:
COMPARING THE MEANS OF TWO RELATED POPULATIONS: The Paired Difference Test
• Related Samples: tests means of 2 related populations à Assume same items will behave alike if treated alike
o Use difference between paired values:
o Assumptions:
§ Both populations are normally distributed
§ Or if not normal, use large enough sample
o Point estimate for paired difference pop mean =
o Sample standard deviation =
• Paired Samples: items are paired together according to some characteristic of interest
o Assume scores are independently selected from a normally
distributed pop.
§
§ Confidence interval estimate:
n
D
D
n
1i
i
å
=
=
1n
)D(D
S
n
1i
2
i
D-
-
=
å
=
Di = X1i – X2i
- n-1 degrees of freedom
- µD = hypothesized mean difference
Document Summary
Chapter 10: fundamentals of hypothesis testing two-sample tests. Comparing the means of two independent populations: difference between two means if unknown, assumptions: Pop is normally distributed or sample sizes are large enough for clt to hold: null hypothesis: h0: 1 - 2 = 0, alternative hypothesis: h1: 1 - 2 0, 1 and 2 assumed equal: Use pooled variance to estimate unknown . Confidence interval: 1 and 2 assumed unequal: Comparing the means of two related populations: the paired difference test: related samples: tests means of 2 related populations assume same items will behave alike if treated alike, use difference between paired values, assumptions: Or if not normal, use large enough sample n i . 1i: point estimate for paired difference pop mean = n, sample standard deviation = n. D: paired samples: items are paired together according to some characteristic of interest, assume scores are independently selected from a normally distributed pop. n-1 degrees of freedom.
