Question

Test the null hypothesis H0:μ=3.3against the alternative hypothesis HA:μ≠3.3, based on a random sample of 37 observations drawn from a normally distributed population with x¯=3.5 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?      YesNoClick for List  

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

Answer 1

Solution :

Given that,

Population mean = = 3.3

Sample mean = = 3.5

Population standard deviation = = 0.89

Sample size = n = 37

This is a two tailed test.

a)

The test statistics,

Z =( - )/ (/n)

= ( 3.5 - 3.3 ) / ( 0.89 / 37 )

= 1.367

b)

P- Value = 2*P(Z > z )

= 2 * ( 1 - P(Z < 1.367)

= 2 * 0.0858

= 0.172

c)

1)

At 5% level of significance,

The p-value is p = 0.172, and since p = 0.172 0.05 , it is concluded that the null hypothesis is fails to reject.

2)

At 10% level of significance,

The p-value is p = 0.172, and since p = 0.172 0.10 , it is concluded that the null hypothesis is fails to reject.