Question

A test is made of H0 : μ = 47 versus H1 : μ > 47. A sample of size n=69 is drawn, and x=48. The population standard deviation is σ=27. Compute the value of the test statistic z.

Answer 1

EXPLANATION

Let's consider the facts:

u=47

H_1 --> u>47

n=69

The standard deviation is 27

The z-score is given by the equation:

`z-\text{score}=(x-\mu)/(\sigma)`

Now,the Test Statistic z is:

`Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt[]{n}}}`

Substituting terms:

`Z=\frac{48-47}{\frac{27}{\sqrt[]{69}}}=\frac{\sqrt[]{69}}{27}`

=0.30765

So, the test statistic z is equal to 0.30765.

The answer is Z=0.30765