Question

Grand Pappy Kenny has been raising cattle on his farm since 1938. Right before he takes the cows to be processed, he weighs them. He figured out that the weights of all the cows he has ever owned follow a Normal distribution. The standard deviation is σ = 182.4 lbs, but he can’t remember the mean µ. He claims that the mean was about 1400 lbs, but he can’t be sure. Pap Ken can skin a muskrat in his sleep but he doesn’t know the first thing about statistical inference. Let’s help him out.

We go out to the field and choose a sample of 10 cows. The weights are given below:

1198.1 1203.2 1012.9 1298.3 1173.2

1302.3 1303.9 1289.4 1158.6 1257.5

Test Pappy’s claim that the mean was µ = 1400 lbs. That is, do a z-test on H0 : µ = 1400, Ha : µ 6= 1400.

Find the z-statistic and the P-value. What can you conclude about his claim?

Answer 1