# Two-tail test

#### toby

##### New Member
For 1996, the U.S. Department of Agriculture has estimated that American consumers would have eaten, on average, 2.6 pounds of cottage cheese throughout the course of that year. Based on a longitudinal study of 98 randomly selected people conducted during 1996, the National Center for Cottage Cheese Studies found an average cottage cheese consumption of 2.75 pounds and a standard deviation of s=14 ounces. Given this information, which of the following statements would be correct concerning a two-tail test at the 0.05 level of significance?

A) We can conclude that the average cottage cheese consumption in America is at least 0.705 pounds more or less than 2.75 pounds per person per year.

B) We can conclude that the average cottage cheese consumption in America truly is 2.6 pounds per person each year

C) We can conclude that the average cottage cheese consumption in America is not 2.6 pounds per person per year.

D) We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.

I found the rejection region to be 0.025 on the left and right side and the area to be 0.95. I also found the average cottage cheese consumption falling between -1.96 to 1.96. I chose answer B. Am I on the right path?

#### tidus

##### New Member
Hi,
I got a test stat of 1.697, which does not fall in the rejection region of >1.96. I would say that we could not reject the null hypothesis.(the null hypothesis is that the mean is 2.6) The data supports the null hypothesis, that the average is 2.6. Our professor would cringe if she saw the "truly" word up there. She has reminded us over and over that we do not know the true value, only what the data say. If you look at the first line of the problem, it says "estimated that....would have eaten 2.6 pounds" . Noone knows the true value. I would have to say that the answer is A. Calculate a 90% confidence interval for the mean of the sample and I bet A is the correct answer.
Again, you always say that the data supports the null hyp. or supports rejecting the null. You'll never be able to say what the true or actual value of a statistic is.
Hope this helps