Question

Consider the following hypothesis test:

Answer 1

Answer:

(a) $t= -1.540$

(b) $0.10 < p < 0.20$

(c) Fail to reject $H_o$

Step-by-step explanation:

Given

$H_o: =18$       $H_a: \ne 18$

$n = 48$

$\bar x = 17$

$\sigma = 4.5$

Solving (a): The test statistic

This is calculated as:

$t= \frac{\bar x - \mu_o}{\sigma/\sqrt n}$

So, we have:

$t= \frac{17 - 18}{4.5/\sqrt{48}}$

$t= \frac{- 1}{4.5/6.93}$

$t= \frac{- 1}{0.6493}$

$t= -1.540$ --- approximated

Solving (b): Range of p value

First, calculate the degree of freedom (df)

$df = n - 1$

$df = 48 - 1$

$df = 47$

Using:

$\alpha = 0.05$ --- significance level

The p value at: $df = 47$ is:

$p = 0.065133$

and the range is:

$0.05 * 2 < p < 2 * 0.10$

$0.10 < p < 0.20$

Solving (c): The conclusion

Compare the p value to the level of significance value

We have:

$p = 0.065133$

$\alpha = 0.05$

By comparison:

$p > \alpha$

because:

$0.065133 > 0.05$

Hence, the conclusion is: fail to reject $H_o$