Question

N =64

Answer 1

Answer:

B.  1.70

Step-by-step explanation:

Given:

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

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

$\textsf{then test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}$

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

$\begin{aligned}\implies z &=\dfrac{65.1-60}{24 / \sqrt{64}}\\\\&=\dfrac{5.1}{3}\\\\&=\dfrac{17}{10}\\\\&=1.7\end{aligned}$