Balance disturbances can be a common source of difficulty for senior citizens. One type of balance test involves standing on one leg, arms crossed and eyes open. The population mean for females, aged 60 - 69, on the balance test is 30 seconds with a σ = 5 seconds. A fitness instructor is implementing a program at her facility, which she calls "Toe the Line," designed to improve balancing skills. After completing the program, a sample of 15 females in the 60 - 69 age group take the balance test. The mean for the sample was M = 32. Using a one-tailed z-test and α = .05, determine whether the program improved balancing skills in older females.
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H₀: μ ≤ 30
H₁: μ > 30
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α ...
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