Answer to Question #342169 in Statistics and Probability for erika miguel

Question

Using thye following information: H_0:=375; H_a: 375; n=100; x = 390; ²=4,900 and a =0.05. is the z-test statistic value equal to 2.14?

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=375$

$H_1:\mu\not=375$

Based on the information provided, $n=100, \bar{x}=390, \sigma^2=4900,$ the significance level is $\alpha = 0.05.$

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{390-375}{\sqrt{4900}/\sqrt{100}}=\dfrac{15}{7}\approx2.14$$