Question

Consider the following:

H₀: μ=10
H₁: μ≠10

For a sample of 6 units, the mean for the sample is 11.2 and the population standard deviation is 2.14.

1)Calculate the p-value for the test.

2) If α=0.10, do you reject the null hypothesis?

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   = 10

Ha :    10

= 11.2

= 2.14

n = 6

1) Test statistic = z =

= ( - ) / / n

= (11.2 - 10) / 2.14 / 6

Test statistic = z = 1.37

P(Z > 1.37 ) = 1-P (Z < 1.37) = 1 - 0.9147 = 0.0853

This is the two tailed test,

P-value = 2 * P(Z > 1.37 )

P-value = 2 * 0.0853

P-value = 0.1706

2) = 0.10  

P-value >

Fail to reject the null hypothesis .