Calories per serving of vanilla yogurt Consumer Reports test

Calories per serving of vanilla yogurt
Consumer Reports tested 6 brands of vanilla yogurt and found the following numbers of calories per serving:

(a) A diet guide claims that you will get 120 calories from serving of vanilla yogurt.Carry out a significance test to see if this sample has a mean calorie content of vanilla yogurt that exceeds 120 calories.State the appropriate H₀ and H_a to test this claim.

H₀: ? < 0 calories; H_a: ? > 0 calories

H₀: ? = 120 calories; H_a: ? >120 calories

H₀: ? = 0 calories; H_a: ? ? 0 calories

H₀: ? > 0 calories; H_a: ? < 0 calories

H₀: ? = 120 calories; H_a: ? ? 120 calories

(b) Carry out the test. Give the P-value. (Round your answer to four decimal places.)

Solution

(a)H₀: ? = 120 calories; H_a: ? >120 calories

------------------------------------------------------------------------------------------------

(b) sample size= n=6

sample mean=103.6667

sample standard deviation =11.48332

The test statisitc is

t=(xbar-mu)/(s/vn)

= (103.6667-120)/(11.48332/sqrt(6))

=-3.48

The degree of freedom =n-1=6-1=5

It is a right-tailed test.

So the p-value= P(t with df=5 >-3.48) =0.9912 (from student t table)