Question

Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothesis that the population mean is greater than 46. The sample size is 25 and alpha =.05. If the sample mean is 50 and the population standard deviation is 8, the observed z value is:
a) 2.5
b) -2.5
c) 6.25
d) -6.25
e) 12.5

Answer 1

Answer:

Option A) 2.5

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 46

Sample mean, $\bar{x}$ = 50

Sample size, n = 25

Alpha, α = 0.05

Population standard deviation, σ = 8

First, we design the null and the alternate hypothesis

$H_{0}: \mu \leq 46\\H_A: \mu > 46$

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{50 - 46}{\frac{8}{\sqrt{25}} } =2.5$

Option A) 2.5