Question

A researcher hired by a farming organization obtains a random sample of 50 cows in a state and finds a 95% confidence interval for the mean milk production for cows to be (22; 30) kg/day. Critique the following interpretations. (a) There is a 95% chance that a cow produces, on average, between 22 and 30 kg of milk per day. (b) We are 95% confident that X(bar) is between 22 and 30 kg of milk per day. (c) The mean milk production(mu) for cows in the state will be 22–30 kg/day images of the time. (d) We are 95% confident cows in this state produce, on average, from 22 to 30 kg of milk per day. (e) In 95% of samples, the mean milk production will be between 22 and 30 kg/day.

Answer 1

Using confidence interval we can estimate the range of population mean $\mu$

Here population under consideration is total number of cows in the "state".

Therefore option d) seems to be correct interpretation of required confidence interval.

d) we are 95% confident that cows in this state produce, on average from 22 to 30 kg of milk per day.