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10 cards from this deck
Xˉ∼N(μ,σ2/n)\bar{X} \sim N(\mu, \sigma^2/n)Xˉ∼N(μ,σ2/n) where σ2\sigma^2σ2 is known and nnn is sample size.
Xˉ∼N(100,72/60)\bar{X} \sim N(100, 7^2/60)Xˉ∼N(100,72/60)
Use Z=(102−100)/7Z = (102-100)/7Z=(102−100)/7; P(Z>0.2857)P(Z > 0.2857)P(Z>0.2857) from Z-table.
It represents the probability of the mean being over 102102102.
H0:μ=21H_0: \mu = 21H0:μ=21, H1:μ>21H_1: \mu > 21H1:μ>21
It identifies values that reject the null hypothesis.
P(Xˉ>21.2)=0.2755P(\bar{X} > 21.2) = 0.2755P(Xˉ>21.2)=0.2755
It indicates insufficient evidence to reject H0H₀H0.
H₀: μ=5\mu = 5μ=5, H₁: μ≠5\mu \neq 5μ=5
Reject H0H_0H0: Mean is significantly different from 555.
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