Question

According to an article by George Will (San Jose Mercury News, Feb. 28, 2002), the average U.S. consumption per person per year of French Fries is 28 pounds. Suppose that you believe that the average in Santa Clara County is not 28 pounds. You randomly survey 50 people in this county. The sample average is 24 pounds with a sample standard deviation of 10 pounds. Conduct an appropriate hypothesis test.

1. This test is:

A. two-tailed

B. no-tailed

C. right-tailed

D. left-tailed

2. The p-value for this test is:

A. 0.0068

B. 0.0034

C. 0.0047

D. 0.0136

3. At the 5% level, the correct conclusion is:

A. The average consumption in Santa Clara County is not 28 pounds.

B. The average consumption in Santa Clara County is less than 28 pounds.

C. The average consumption in Santa Clara County is less than 24 pounds

D.  The average consumption in Santa Clara County is 24 pounds

Answer 1

(1) right choice is A. two-tailed

here we would like to test the claim of believe that the average in Santa Clara County is not 28 pounds, so alternate hypothesis would be Ha: so this is two tailed test. whether test is left tailed, right tailed or two tailed depends on alternate hypothesis

(2) right choice is A. 0.0068

here we use t-test and statistic t=|(-)|/=|(24-28)|/(10/sqrt(50))=|-2.8284|=2.8284 with n-1=50-1 =49 df

p-value=0.0068 ( using ms-excel=tdist(2.8284,49,2))

(3) right choice is A. The average consumption in Santa Clara County is not 28 pounds.

here we want to test the null hypothesis H0: =28 and Ha:,

since p-value =0.0068 is less than level of significance =0.05 , so we reject H0 ( or fail to accept) in favor of alternate hypothesis Ha:  and conclude that The average consumption in Santa Clara County is not 28 pounds.