Question

9

Test the null hypothesis Ho : u = 3.0against the alternative hypothesis HA: U < 3.0 , based on a random sample of 25 observations drawn from a normally distributed population with ū = 2.8 and o = 0.70. a) What is the value of the test statistic? Round your response to at least 3 decimal places. Number b) What is the appropriate p-value? Round your response to at least 3 decimal places. Number c) Is the null hypothesis rejected at: i) the 10% level of significance? Click for List ii) the 5% level of significance? Click for List

Answer 1

Solution :

$\mu$= 3.0

$\bar x$ =2.8

$\sigma$ =0.70

n = 25

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 3.0

H_a : $\mu$ <3.0

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$ / $\sqrt$ n

= (2.8-3.0) / 0.70 / $\sqrt$ 25

=−1.429

P(z < -1.43) = 0.0764

P-value = 0.077,

$\alpha$ = 0.10

P-value < $\alpha$

p=0.077,<0.10, it is concluded that the null hypothesis is rejected.

when

$\alpha$ = 0.05

P-value < $\alpha$

p=0.077,>0.05, it is concluded that the null hypothesis is not rejected.