Question

N =64

x bar = 65.1
σ = 24
h₀: μ = 60
h‎ₐ: μ ≠ 60

The test statistic equals ____

A. -1.70
B. 1.70
C. 0.3904
D. 0.0446

Answer 1

B. 1.70

Explanation:

Given:

• 
  `n=64`
• 
  `\overline{x}=65.1`
• 
  `\sigma=24`
• 
  `\textsf{h}_0:\mu=60`
• 
  `\textsf{h}_1:\mu\\eq 60`

`\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,(\sigma^2)/(n)\right) \implies Z=\frac{\overline{X}-\mu}{\sigma / √(n)} \sim \textsf{N}(0,1)`

`\textsf{then test statistic is}: \quad z=\frac{\overline{x}-\mu}{\sigma / √(n)}`

Substituting the given values into the formula to find the test statistic z:

`\begin{aligned}\implies z &=(65.1-60)/(24 / √(64))\\\\&=(5.1)/(3)\\\\&=(17)/(10)\\\\&=1.7\end{aligned}`