Question

Consider the hypotheses shown below. Given that x overbar= 48 ​,sigma=13 ​, n=33​, alpha=0.10 ​, complete parts a and b.

Upper H 0​: mu less than or=45

Upper H 1​: mu greater than 45

a. What conclusion should be​ drawn?

b. Determine the​ p-value for this test.

a. The​ z-test statistic is .

​(Round to two decimal places as​ needed.)

Answer 1

Given that, sample size ( n ) = 33

sample mean $(\bar x)$ = 48

population standard deviation $(\sigma)$ = 13

significance level $(\alpha)$ = 0.10

The null and the alternative hypotheses are,

$H_0: \mu \leq 45$

$H_1: \mu > 45$

Test statistic is,

$Z = \frac { \bar x -\mu}{\frac { \sigma}{\sqrt { n }}}= \frac { 48-45}{\frac { 13}{\sqrt { 33}}}= 1.33$

Test statistic is 1.33

p-value = P(Z > 1.33) = 1 - P(Z < 1.33) = 1 - 0.9082= 0.0918

p-value = 0.0918

Here, p-value = 0.0918 < $\alpha = 0.10$

So, we reject the null hypothesis ( H₀).