Chapter 12, Problem 20PT

To determine

To perform the hypothesis testing for the given data.

Answer to Problem 20PT

Fail to reject the Null hypothesis.

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:\mu =65\\ H_1:\mu <65\\ \\ n=120\\ \overline{x}=64.8\\ s=2.1\end{array}$

Formula used:

  $t=\frac{\overline{x}-\mu }{\frac{s}{\sqrt{n}}}$

Calculation:

  $\begin{array}{l}t=\frac{64.8-65}{\frac{2.1}{\sqrt{120}}}\\ t=-1.04\end{array}$

Now,

Critical value:

  $\begin{array}{l}{t}_{\left(n-1,\alpha \right)}\\ =t_{\left(120-1,0.05\right)}\\ =-1.645\end{array}$

  

• Here, the one (Left) tailed hypothesis test (t test) is conducted at the level of alpha = 0.05.
• The test statistics value -1.04 is higher than the critical value -1.645, which means it does not falls in rejection region.
• Therefore, we have enough evidence to fail to reject the null hypothesis.
• Which means the Mean is equal to 65.