City University of Hong Kong
MA 2172
MA2172 Applied Statistics for Sciences and Engineering Examples on Chapter 8 - Hypothesis Test: One-Tailed – Full Solution 1. (i) r H0 : µ ≥ 572 calories/h : µ < 572 calories/hr Ha σ = 45 , n = 36 , x = 557 , α = 0.01 2 36 45 557 572 Test -statistic, = − − = − =∗ n x z σ µ Critical value = −z(0.01) = −2.33 As ∗ z is
...[Show More]
MA2172 Applied Statistics for Sciences and Engineering Examples on Chapter 8 - Hypothesis Test: One-Tailed – Full Solution 1. (i) r H0 : µ ≥ 572 calories/h : µ < 572 calories/hr Ha σ = 45 , n = 36 , x = 557 , α = 0.01 2 36 45 557 572 Test -statistic, = − − = − =∗ n x z σ µ Critical value = −z(0.01) = −2.33 As ∗ z is not in the critical region, we fail to reject H0 . There is insufficient evidence, at 0.01 level of significance, that the average number of calories burned is actually less than 572. (ii) Let c x be the critical value of the sample mean. Then 2.33 36 45 572 = − xc − ⇒ xc = 554.525 ( 1.67) 0.0475 36 45 554.525 542 ( ) = > = − = P x > x = P z > P z β c 2. (i) 8 : 10. H0 µ ≤ Ha : µ >10.8 σ = 3, n = 36 , x =12.2 , α = 0.01 2.8 36 3 12.2 10.8 Test -statistic, = − = − =∗ n x z σ µ Critical value = z(0.01) = 2.33 As ∗ z is in the critical region, we reject H0 . (ii) n x x z c σ = - critical = µ + (0.01) 11.965 36 3 = 10.8 + 2.33× = Let µ1 be the actual average. Then, ( ) 12.48
[Show Less]
-preview.jpeg)
-preview.jpeg)
-preview.jpeg)
