STATISTICS FOR MANAGERS

Answers, Ch. 10

10.7

a. 

1 = thought about cheesecake first, 2 = thought about organic fruit salad first

H₀:  m₁ ≥ m₂  =>  H₀:  m₁ - m₂ ≥ 0
H₁:  m₁ < m₂ =>   H₁:  m₁ - m₂ < 0

d.

α = 0.01, n₁ = 20, n₂ = 20

tSTAT =

 α = 0.01, d.f. = n₁ + n₂ - 2 = 20 + 20 - 2 = 38 => Reject H₀ if t_STAT  < 2.4286

= 17992

=> Reject H₀, accept H₁

10.29 (8th Edition)

1 = men, 2 = women

a.

H₀:  π₁ = π₂  =>  H₀:  π₁ - π₂ = 0
H₁:  π₁ ≠ π₂ =>   H₁:  π₁ - π₂ ≠ 0

α = 0.01, n₁ = 542, n₂ = 543

ZSTAT =

α = 0.01 => Reject H₀ if Z > 2.576 or < -2.576

p₁ = x₁ / n₁ = 238 / 542 = 0.4391, p₂ = x₂ / n₂ = 276 / 543 = 0.5083

= -2.28 not > 2.576 and not < -2.576

=> Do not reject  H₀

b.  P-value = 2 * P (Z < -2.28) = 2 * 0.0113 = 0.0226

The lowest value of α where the null hypothesis can be rejected is 0.0223

.

10.33 (8th Edition)

1 = B2B, 2 = B2C

a.

H₀:  π₁ = π₂  =>  H₀:  π₁ - π₂ = 0
H₁:  π₁ ≠ π₂ =>   H₁:  π₁ - π₂ ≠ 0

α = 0.01, n₁ = 542, n₂ = 543

ZSTAT =

α = 0.05 => Reject H₀ if Z > 1.96 or < -1.96

p₁ = x₁ / n₁ = 344 / 390 = 0.882, p₂ = x₂ / n₂ = 373 / 610 = 0.611

ZSTAT =

= 9.28  > 1.96, not < -1.96

=> Reject  H₀, accept H₁

b.  P-value = 2 * P (Z > 9.28) = 2 * 0.0000 = 0.0000

The lowest value of α where the null hypothesis can be rejected is 0.0000