1Calories per serving of vanilla yogurt Consumer Reports tes

1)Calories per serving of vanilla yogurt
Consumer Reports tested 20 brands of vanilla yogurt and found the following numbers of calories per serving:

(a) Find the mean. (Round your answer to two decimal places.)
calories

(b) Find the margin of error for 95% confidence. (Round your answer to four decimal places.)
calories

(c) Report the 95% confidence interval for ?, the mean calorie content of vanilla yogurt. (Round your answers to four decimal places.)

calories, calories

37.7	38.4	51.4	44.0	38.3	45.5	44.6	35.5	48.9	44.2
45.3	48.4	47.2	44.1	49.1	42.6	43.3	45.7	47.8	40.4

1)Calories per serving of vanilla yogurt Consumer Reports tested 20 brands of vanilla yogurt and found the following numbers of calories per serving: 37.7 38.4 51.4 44.0 38.3 45.5 44.6 35.5 48.9 44.2 45.3 48.4 47.2 44.1 49.1 42.6 43.3 45.7 47.8 40.4 (a) Find the mean. (Round your answer to two decimal places.) calories (b) Find the margin of error for 95% confidence. (Round your answer to four decimal places.) calories (c) Report the 95% confidence interval for ?, the mean calorie content of vanilla yogurt. (Round your answers to four decimal places.) calories, calories

Solution

(a) mean=44.12

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(b) the degree of freedom =n-1=20-1=19

sample standard deviation =4.273369

Given a=1-0.95= 0.05, t(0.025, df=19) =2.093 (from student t table)

So margin of error =t*s/vn

=2.093*4.273369/sqrt(20)

=1.999975

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(c) So the lower bound is

xbar- t*s/vn = 44.12-1.999975 =42.1200

So the upper bound is

xbar + t*s/vn =44.12+1.999975 =46.11997