Question

1. A random sample of 14 cows was selected from a large dairy herd. The milk yield in one week was recorded (in kilograms) for each cow. From this sample of 14 cows, the sample mean and sample standard deviation are 140.21 and 22.6, respectively. Assuming the distribution of milk yields is Normal, use a hypothesis test to investigate the claim that the true mean weekly milk yield for the herd is greater than 120 kg. Use an alpha-level of .01.

Answer 1

Solution :

This is the right tailed test,  

The null and alternative hypothesis is ,

H0 :   = 120

Ha : > 120

Test statistic = t =

= ( - ) / s / n

= (140.21 - 120) / 22.6 / 14

Test statistic = t = 3.35

degrees of freedom = n - 1 = 14 - 1 = 13

P(t > 3.35) = 1-P (t < 3.35) = 1 - 0.9974

P-value = 0.0026

= 0.01  

P-value <

Reject the null hypothesis .