Question 4. The normal mean content of lysine in cow\'s milk is known to be 275

Question

Question 4. The normal mean content of lysine in cow's milk is known to be 275 mg/100 mL and the distribution is believed to be approximately normal. Twenty cows were placed on an experimental ration expected to increase lysine in the milk if in fact it had any effect at all on lysine. The data is as follows: 253 268 277 262 280 284 318 258+ 314 293 311 305 299+ 301 322+ 272++ 285^ 291 296290+ a) Can one be confident, based on a Type I error rate of 1%, that the true mean milk lysine for cows fed this ration exceeds 275 mg/100 mL? b) Suppose that, in attempting to publish the results, you are told by an editor that the study is "not publishable: no control". To address this limitation, propose an alternative design also based on the use of 20 cows.

Explanation / Answer

a) sample mean = 288.95

sample sd = 19.98809

Ho: mu = 275

HA: mu > 275

TS = (Xbar =mu)/(s/sqrt(n))

= (288.95 -275)/(19.98809/sqrt(20))

=3.12117

degree of freedom = n-1 =20- 1 = 19

p-value = P(t > 3.12117) = 0.00281

since p-value < alpha (0.01)

we reject the null and conclude that there is significant evidence that the mean is more than 275

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