Dairy cows at large commercial farms often receive injections of bST (Bovine Somatotropin), a hormone used to spur milk production. Bauman et al. (Journal of Dairy Science, 1989) reported that 12 cows given bST produced an average of 28.0 kg/d of milk. Assume that the standart deviation of milk production is 2.25 kg/d. (a) Find a 99% confidence interval for the true mean milk production. Round your answers to two decimal places (e. g. 98.76).

The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Z-table as such z has a p-value of .

That is z with a pvalue of , so Z = 2.575.

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d.

The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d.

The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d.

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step-by-step explanation: