Question

The health of employees is monitored by periodically weighing them in. A sample of n = 54 employees has a mean weight of x̄ = 190 lb. Assuming that σ = 25 lb, use a 0.01 significance level to test the claim that the population mean of all such employees weights is less than 200 lb.

Group of answer choices

a. H₀: μ = 200; H₁: μ < 200; Test statistic: z = -2.94. P-value: 0.0016. Since the P-Value is smaller than the significance level of 0.05, we reject H₀. There is sufficient evidence to support the claim that the mean is less than 200 pounds.

b. H₀: μ = 190; H₁: μ > 190; Test statistic: z = 2.94. P-value: 0.9984. Since the P-Value is larger than the significance level of 0.05, we fail to reject H₀. There is not sufficient evidence to support the claim that the mean is greater than 190.

Answer 1

Given n=54, X=190, =25 Hoil = 200 vs till < 200 Test statistic Zeal 190-200 الد oli 2554 Zcal = -2.93939-2.94 Izcall 2.94 P-value = P(Z <-2.94) = 0.0016 ... p-value <<ie., 0.0016<0.01 then Reject to. Q) Ho: U= 200; Hill <200. Test statistic Z=-2.94. P-value 0.006, since the P-value is smaller than the significance level of 0.01, reject Ho. There is sufficient evidence to support the claim that the mean is less than 200 pounds. ave