Hyp we suspect it is less than 50 step 2 calculate

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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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