In testing H₀: µ $\le$ 23 versus H_A: µ 23 when = 26,s = 6,and n = 30,what is the value of the z-statistic? A)-2.74 B)15.00 C)1.09 D)2.74

Question

In testing H₀: µ $\le$ 23 versus H_A: µ > 23 when = 26,s = 6,and n = 30,what is the value of the z-statistic? A)-2.74 B)15.00 C)1.09 D)2.74

Quizplus · Accepted Answer

First, we need to calculate the sample mean and standard deviation: x̄ = 26 s = 6 n = 30 Next, we need to calculate the z-statistic using the formula: z = (x̄ - µ) / (s / √n) For the null hypothesis H₀, µ = 23: z = (26 - 23) / (6 / √30) = 2.74 Since the alternative hypothesis is µ > 23, we only need to look at the right-hand side of the standard normal distribution table. The value for z = 2.74 is 0.9966, which means the probability of observing a sample mean of 26 or higher if the true population mean is 23 is 0.0034. This is a low probability, so we reject the null hypothesis in favor of the alternative hypothesis. Therefore, the value of the z-statistic is 2.74.

In Testing H0: µ ≤\le≤ 23 Versus HA: µ > 23 When = 26,s

In Testing H₀: µ $\le$ 23 Versus H_A: µ > 23 When = 26,s