Chapter 12.6, Problem 31HP

To determine

To Define: whether the statement is sometimes, always or never true.

Answer to Problem 31HP

The given statement is always true.

Explanation of Solution

Given information:

If confidence interval contains hypothesized value then one cannot reject the null hypothesis.

Otherwise null hypothesis will be rejected.

Calculation:

The formula used for $95\text{\%}$ confidence interval is,

  $\overline{x}\pm 1.96\cdot \frac{s}{\sqrt{n}}$

Let $u$ shows the hypothesized value. Let ${\mu }_0$ shows the hypothesized value.

If confidence interval contains hypothesized value then one cannot reject the null hypothesis.

Otherwise null hypothesis will be rejected.

Hence, given statement is true.