BA 253: Business Statistics 10/22/08
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Hypothesis Testing Start ICE 7
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Chapter 9: Hypothesis Testing
Use statistical evidence to answer questions.
Formal methodology.
Never “prove” or “disprove” a claim. Rather, show that statistical evidence either
supports or refutes the claim.
Ex A: A report states that typical college students spend about 2 hours per day working
on a computer. Is this true at FLC?
Claim: μ = 2 hours/day.
Collect data: If
x
= ½ or
x
= 3.5, obviously no.
Survey FLC students and find that
x
= 1.87 and s = 0.76.
Does the data support or refute the claim that the mean is 2 hours???
Confidence Interval Answer
Assume 95% confidence (5% chance of error)
CI = (1.66, 2.08). What does this tell us?
Since μ = 2 is in the interval, the evidence supports the claim. (But does not
“prove” it!)
Final answer: FLC students appear to spend about 2 hours per day on a computer,
same as the national average.
Formal Hypothesis Testing Answer
H0: μ = 2 (null hypothesis)
Ha: μ ≠ 2 (alternative hypothesis)
α = 5% (chance of error = 1 – confidence = 1 – 95%)
Need two things: Critical Value(s) and Test Statistic
Show how zcrit = ± 1.96 with table, accept, reject.
Calculate zstat = = -1.21
Since zstat is in acceptance region, accept H0, the mean appears to be 2 hours.
p-value
Calculate p-value = 22%.
If H0 is really true (μ = 2), then there is a 22% chance that we would see a sample
mean with
x
≤ 1.87 ( or
x
≥ 2.13). A 22% chance is not that unlikely, so accept
H0.
In other words, accept H0 if p-value ≥ α, reject H0 if p-value ≤ α.
