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Unformatted text preview: 1 out of 100 times (signiﬁcant level α = 1%) then we have reasons to
believe that µ = 50 (i.e., we reject the Null Hypothesis)
Rafael Mendoza
Elementary Business Statistics – Class 14 McCombs 5 Steps to determine the Hypothesis Test
Step 1 Identify the Hypothesis
H0 : µ = 50, (Null Hyp: In Average UT students have $50 in cash)
Ha : µ < 50, (Alt. Hyp: We suspect it is less than $50)
Step 2 Calculate the test statistic (z )
The sample has a mean x = $49 and x ≈ N (50, 0.5) thus,
¯
¯
We normalize
x−µ
¯
49 − 50
z= √ =
= −2
0 .5
σ/ n
Step 3 Calculate the P value
(Prob. of observing a value
Less or equal to x, given that
¯
H0 is true, i.e., given that
x ≈ N (50, 0.5). Equivalently,
¯
Prob. of observing a value
z ≤ −2, given that
z ≈ N (0, 1).) P [z ≤ −2] = 0.0228 or P value = 2.28%
0.4 0.3 Area 0.0228
0.2 0.1 4 z ...
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 Fall '07
 Gemberling
 Statistics

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