STATISTICS FOR MANAGERS

Answers, Ch. 9

9.16

a.

Z =

" = 0.01 => Z = 2.576 => Reject H₀ if Z_STAT > 2.576 or < -2.576

Z_STAT = = -1.77 2.576 and -2.576

=> Do not reject H₀

b.  P-value = 2 * P (Z < -1.77) = 2 * 0.0384 = 0.0768

The lowest level of " where the H₀ can be rejected is 0.0768.

c.  See 8.9a

0.988 < µ < 1.002

d.  The results are consistent.  The test was a two-tailed test, and the probability content and the level of α are complementary.  The hypothesized value was inside the confidence interval, so the null hypothesis should not be rejected, and it wasn't.

9.49

a.

t_STAT =  

" = 0.05, d.f. = 36 - 1 = 35 => t_CRIT = 1.6896 => Reject H₀ if t_STAT < -1.6896

t_STAT = = -2.60 < -1.645

=> Reject H₀, accept H₁

b. 

t_STAT =

t_STAT = = -2.60

P-value = P (t_n-1 < -2.60) = 0.0069 (from computer)

P-value < " => Reject H₀, accept H₁

c.  The lowest level of " where the H₀ can be rejected is 0.0069.

d.  The results are consistent.

9.27

t_STAT =

" = 0.05, d.f. = 18 - 1 = 17 => t_CRIT = 2.1098 => Reject H₀ if t_STAT > 2.1098 or < -2.1098

t_STAT = = -0.9318 2.1098 and -2.1098

=> Do not eject H₀

b.  P-value = 2 * P (t < -0.93) = 0.3645 (from computer)

The lowest level of " where the H₀ can be rejected is 0.3645.

9.59

a.

Z =

P = X / n = 135 / 500 = 0.27

" = 0.05 => Reject H₀ if Z_STAT > 1.645

Z_STAT = = 3.91 > 1.645

=> Reject H₀, accept H₁