Confidence intervals and sample size, part 2. A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics:

y  =  $4.49   SE1y2  = $0.06

a) Find a 95% confidence interval for the mean price of regular gasoline in that region.

b) Find the 90% confidence interval for the mean.

c) If we had the same statistics from a sample of 60 sta- tions, what would the 95% confidence interval be now?

weight gain in livestock. Their researchers report that the 77 cows studied gained an average of 56 pounds and that a 95% confidence interval for the mean weight gain this sup- plement produces has a margin of error of ; 11 pounds. Staff in their marketing department wrote the following conclusions. Did anyone interpret the interval correctly? Explain any misinterpretations.

a) 95% of the cows  studied  gained  between  45  and 67 pounds.

b) We're 95% sure that a cow fed this supplement will gain between 45 and 67 pounds.

c) We're 95% sure that the average weight gain among the cows in this study was between 45 and 67 pounds.

d) The average weight gain of cows fed this supplement is between 45 and 67 pounds 95% of the time.

e) If this supplement is tested on another sample of cows, there is a 95% chance that their average weight gain will be between 45 and 67 pounds.