Question

A screen-printing business has to choose between printing t-shirts and

sweatshirts to manage risk due to dwindling student enrollments. The matrix below

shows the returns of each shirt and probabilities of three possible enrollment outcomes; high,

average, and low.

Student Enrollment Outcome	Probability	Corn	Soybeans
High	0.1	$25,000	$29,000
Average	0.6	12,000	15,000
Low	0.3	5,000	2,000
Expected Value		11,200	12,500
Minimum Value		$5,000	$2,000
Maximum Value		$25,000	$29,000
Range		$20,000	$27,000

Which shirt type should the business produce considering each of the following decision rule?

i. Most likely outcome                        ______________________________

ii. Maximum expected value ______________________________

iii. Risk and returns comparison             ______________________________

iv. Safety first (maxi-min)      ______________________________

v. Minimum of $4,000 returns            ______________________________

Answer 1

1)a) Option - A) Matched pairs

b) Option - C) < 0

c) = ((-3) + 0 + 2 + (-6) + (-1) + (-3) + (-3) + 0 + (-3) + (-4))/10 = -2.1

s_d = sqrt((((-3 + 2.1)^2 + (0 + 2.1)^2 + (2 + 2.1)^2 + (-6 + 2.1)^2 + (-1 + 2.1)^2 + (-3 + 2.1)^2 + (-3 + 2.1)^2 + (0 + 2.1)^2 + (-3 + 2.1)^2 + (-4 + 2.1)^2)/9) = 2.331

c) The test statistic t = ( - D)/(s_d/)

                                 = (-2.1 - 0)/(2.331/)

                                = -2.85

d) P-value = P(T < -2.85)

                  = 0.0095

e) Since the P-value is less than the significance level(0.0095 < 0.05), so we should reject H₀.

Yes, there is sufficient evidence to support the claim that people do better on the second test.

2) At 95% confidence interval the critical value is t^* = 2.262

The 95% confidence interval is

+/- t^* * s_d/

= -2.1 +/- 2.262 * 2.331/

= -2.1 +/- 1.667

= -3.767, -0.433