Question

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ<3.8, based on a random sample of 25 observations drawn from a normally distributed population with x¯=3.6 and σ=0.72.

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?      YesNoClick for List  

ii) the 5% level of significance?      NoYesClick for List  

Answer 1

Solution :

= 3.8

=3.6

=0.72

n = 25

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :    = 3.8

H_a : < 3.8

a ) Test statistic = z

= ( - ) / / n

= (3.6-3.8) / 0.72 / 25

= -1.39

Test statistic = z = -1.39

b ) P(z < -1.39 ) =0.082

P-value =0.082

c ) = 0.10

P-value <

0.082 < 0.10

Reject the null hypothesis .

There is sufficient evidence to suggest that

= 0.05  

P-value >

0.082 > 0.05

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that