Question

According to a USA Today 2018 study the average adult in Montana drinks 40.8 gallons of beer in a year (1st in the country, New Hampshire was the 2nd most with 39.8 gallons per year, and North Dakota and South Dakota are tied for 3rd with 38.2 gallons on average per year). Suppose the Montana Brewer’s Association (MBA) think that this number is actually higher. In a survey of 42 random Montana adults they found the mean gallons drunk to be 42.0 and the standard deviation to be 4.4 gallons.

(e) Calculate an approximate 95% confidence interval for the mean gallons of beer drunk by all Montana adults. Suppose MBA was now interested if on average Montanan adults drink a different amount than 40.8 gallons. Is the sample result significant at a significance level of .05 based on this confidence interval?

(f) Interpret this confidence interval in the context of the problem. Circle all true statements.

i. There is a 95% probability that the mean gallons of beer drunk by Montanans in a year is in the interval given above.

ii. We are 95% confident that the number of gallons of beer drunk by each Montanan in a year is in the interval given above.

iii. We are confident that 95% of the time, the mean gallons of beer drunk by Montanans in a year is in the interval given above.

iv. We are 95% confident that the mean gallons of beer drunk by Montanans in a year is in the interval given above.

(g) State, very carefully, the assumptions necessary for the significance test and confidence interval used above to be valid. 3

Answer 1