Question

Test the null hypothesis H0:μ=3.8against the alternative hypothesis HA:μ≠3.8, based on a random sample of 35 observations drawn from a normally distributed population with x¯=4 and σ=0.89.

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 5% level of significance?      NoYesClick for List  

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

Answer 1

Solution :

= 3.8

=4

=0.89

n = 35

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 3.8

H_a :     3.8

a ) Test statistic = z

= ( - ) / / n

= (4 -3.8) / 0.89 / 35

= 1.33

Test statistic = z = 1.33

b ) P(z >1.33 ) = 1 - P(z < 1.33 ) = 1 -0.9082

P-value =2 *0.0918 =0.184

c ) = 0.05  

P-value >

0.184 > 0.05

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that

= 0.10

P-value >

0.184 > 0.10

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that