Suppose that for the population of Canada the average daily consumption of sugar is grams (or teaspoons) with standard deviation = grams. A research study collects data from a random sample of Canadians.
(a)
Consider that the sampling distribution of the sample mean follows the normal distribution. Find the probability that the sample mean differs from the population mean by more than grams. To get the answer find the shaded area shown in the graph. Round your answer to two decimal places.
(b)
When the sample size is increased, the population standard deviation will:
A.
decrease
B.
stay the same
C.
increase
(c)
Suppose the population standard deviation was grams instead of grams. Which of the following graphs depicts how this will change the shape of the sampling distribution of the sample mean?
Choose
(1)
(2)
(1)
(2)
(Click on a graph to enlarge it.)
(d)
If the population standard deviation increases, the probability that the sample mean differs from the population mean by more than grams (the calculation in (a)) will:
A.
decrease
B.
increase
C.
stay the same
You can earn partial credit on this problem.