Question

Test the null hypothesis H0:μ=3.3against the alternative hypothesis HA:μ<3.3, based on a random sample of 25 observations drawn from a normally distributed population with x¯=3.1 and σ=0.68.

a) What is the value of the test statistic?

Round your response to at least 3 decimal places.

   

b) What is the appropriate p-value?

Round your response to at least 3 decimal places.

   

c) Is the null hypothesis rejected at:

i) the 10% level of significance?      NoYesClick for List  

ii) the 5% level of significance?

Answer 1

Test statistic = z

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

= (3.1 - 3.3) / 0.68 / $\sqrt$ 25

Test statistic = -1.471

P-value = 0.071

(i)

At 5%

P-value < $\alpha$

Reject the null hypothesis .

(ii)

At 10%

P-value > $\alpha$

Fail to reject the null hypothesis .