Question

(8) It has been long believed that eating oatmeal regularly lowers blood cholesterol. To test this claim, a scientist with the FDA measured the change in blood cholesterol levels of a randomly chosen sample of 25 people of a certain age group (who ate oatmeal for breakfast for a month) and found a sample-average reduction of 15 points with a standard deviation of 6 points. Is it believable at a 5% significance level that the population-mean reduction in all people of that age group is more than 10 points? [Hint: First construct a 95% lower confidence bound for the population mean and then see if the number 10 is below it.]

Answer 1

Solution:

n = 25

= 15

s = 6

We construct 95% lower confidence bound for the population mean.

c = 95% = 0.95

= 1 - c = 1 - 0.95 = 0.05

df = n - 1 = 25 - 1 = 24

Critical value is

The one sided lower confidence bound is given by

15 - {1.711 * 6/25 ]

15 - 2.0532

12.9468

Now , hypothetical value 10 is below 12.9468.

So , we can conclude that the population-mean reduction in all people of that age group is more than 10 points.

Yes , it is believable at a 5% significance level that the population-mean reduction in all people of that age group is more than 10 points.