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# Stats - Section 8 3 z Test for a Mean Chapter 8 Hypothesis...

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Unformatted text preview: Section 8- 3 z Test for a Mean Chapter 8 Hypothesis Testing Section 8- 3 Chapter 8 Hypothesis Testing A report in USA TODAY stated that the average age of commercial jets in the United States is 14 years. An executive of a large airline company selects a sample of 36 planes and finds the average age of the planes is 11.8 years. The standard deviation of the sample is 2.7 years. At α = 0.01 , can it be concluded that the average age of the planes in his Company is less than the national average? C . V . = – 2.33 z = X – μ s n = 11.8 – 14 2.7 36 = – 4.89 – 2.33 – 4.89 μ ≥ H : 14 H 1 : μ < 14(claim) Reject the null hypothesis. There is enough evidence to support the claim that the average age of the planes in the executive’s airline is less than national average. C . V . = – 2.33 μ ≥ H : 14 H 1 : μ < 14(claim) z = X – μ s n = 11.8 – 14 2.7 36 = – 4.89 Decision Rule: Reject H if -4.89 < -2.33 Reject Ho Section 8- 3 Chapter 8 Hypothesis Testing The average one-year-old (both sexes) is 29 inches tall. A random sample of 30 one-year-olds in a large day care franchise resulted in the following heights. At α = 0.05 , can it be concluded that the average height differs from 29 inches? 2 5 32 35 25 30 26. 5 26 25.5 29. 5 32 3 28. 5 30 32 28 31. 5 29 29.5 30 34 2 9 32 27 28 33 28 27 32 29 29. 5 – 1.96 0 1.96 C . V . = ± 1.96 0.944 z = X – μ σ n = 29.45 – 29 2.61 30 s = 2.61 X = 29.45 = 0.944 H : μ = 29 μ ≠ H : 29 ( ) 1 claim Decision Rule: Reject H if |0.944|> 1.96 (Which is the same as saying, Reject H if 0.944 < -1.96 OR 0.944> 1.96) Do not reject the null hypothesis. There is not enough evidence to support the claim that the average height differs from 29 inches. C . V . = ± 1.96 z = X – μ σ n = 29.45 – 29 2.61 30 s = 2.61 X = 29.45 = 0.944 H : μ = 29 μ ≠ H : 29 ( ) 1 claim Section 8- 3 Exercise #13 Chapter 8 Hypothesis Testing To see if young men ages 8 through 17 years spend more or less than the national average of \$24.44 per shopping trip to a local mall, the manager surveyed 33 young men and found the average amount spent per visit was \$22.97 . The standard deviation of the sample was \$3.70 . At α = 0.02 , can it be concluded that the average amount spent at a local mall is not equal to the national average of \$24.44 . = – 2.28 = 22.97 – 24.44 3.70 33 C.V. = ± 2.33 – 2.33 2.33 H : μ = \$24.44 μ ≠ H : \$24.44 (claim) 1 n = 33 X = \$22.97 s = \$3.70 s = \$3....
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Stats - Section 8 3 z Test for a Mean Chapter 8 Hypothesis...

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