question (1)

Assume that the differences are normally distributed.

Observation	1	2	3	4	5	6	7
	7.6	7.6	7.4	5.7	8.3	6.6	5.6
	8.1	6.6	10.7	9.4	7.8	9.0	8.5

a) Determine = for each pair of data.

b) Compute and .

c) Test if < at the = . level of significance.

d) Construct a 95% confidence interval about the population

mean difference .

question (2)

Test whether > at the = . level of significance for the given sample data.

	Sample 1	Sample 2
n	23	13
x	43.1	41
s	4.5	5.1

question (3)

According to the manufacturer of M&Ms, 12% of the peanut M&Ms in a bag should be brown, 15% yellow, 12% red, 23% blue, 23% orange, and 15% green. A student randomly selected a bag of peanut M&Ms. The student counted the number of M&Ms that were each color and obtained the results shown in the table below. Test whether peanut M&Ms follow the distribution stated by M&Ms at 0.05 level of significance.

colour	Frequency
brown	53
yellow	66
red	38
blue	96
orange	88
green	59

a) Stat H0 and H1.

b) Calculate expected values for all colors.

c) Calculate test statistics.

d) Find critical value for chi-square.

e) Find P-value.

f) Make appropriate statistical and managerial decisions.