One-Sample t and z Tests for Population Means
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Hypothesis Tests for Population Means
Test 1: Sample of 10 — Mean < 550
(a) In a random sample of 10 people who take a test, the average score is 532.4, and the standard deviation is 28.3. Do the data provide significant evidence, at the 5% level, that the population mean score is less than 550?
- Step 1: Hypotheses.
H0: μ = 550 vs. Ha: μ < 550 (1 point) Where μ is the population mean score.
- Step 2: Significance level.
α = 0.05 (1 point)
- Step 3: Test statistic.
Test Statistic: tobs = (X̄ − μ0)/(s/√n) = (X̄ − 550)/(s/√n) (1 point)
- Step 4: Rejection region.
The test rejects H0 at level α in favor of Ha if tobs < −tα,df=9, where t is based on 9 degrees of freedom. (1 point)
- Step 5: Calculation and conclusion.
Test Statistic:

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