2000 Flex-Time and Flex-Mode Prob-Stat I Hypothesis Testing Problems Page

45-733 Probability and Statistics I (3rd Mini AY 1999-2000 Flex-Mode and Flex-Time)

Practice Hypothesis Testing Problem Answers

10.5(a)

, where a = 0.01, a/2 = 0.005, Z_0.005 = 2.58

(b) Reject if

(c) Test statistic is :

Since, -2.58 < -1.77 < 2.58 DO NOT REJECT H₀

10.7

, where a = 0.05, -Z_a= -1.645

Reject if

Test statistic is:

Since, -4.22< -1.645 REJECT H₀

10.9

, where a = 0.01, a/2 = 0.005, and Z_0.005 = 2.58

Reject if

Test statistic is:

Since, 3.65> 2.58 REJECT H₀

10.10 (a)

, where a = 0.01, Z_0.01 = 2.33

(b) One tailed test

(c) Reject if

Test statistic is:

Since, 9.56> 2.33 REJECT H₀

10.11(a)

, where a = 0.1, a/2 = 0.05, Z_a/2 = 1.645

(b) One tailed test

(c) Reject if

Test statistic is:

Since, -1.645 < -0.954 < 1.645 DO NOT REJECT H₀

10.12 (a)

, where a= 0.05, a/2 = 0.025, Z_0.025 = 1.96

Reject if

Test statistic is:

Since, 3.07 > 1.96 REJECT H₀

(b) Columnist’s claim is too low

10.15(a)

, where a = 0.01, a/2 = 0.005, Z_0.005 = 2.58

Reject if

On assumption that p₁ = p₂, best estimate for the denominator is to set

= 0.606

Test statistic is :

Since, 10.65 > 2.58 REJECT H₀.

10.58

, where a = 0.05, a/2 = 0.025, t_0.025= 2.131 (15 degrees of freedom)

Reject if

Test statistic is:

Since, -2.131 < 0.1< 2.131 DO NOT REJECT H₀

10.65

, where a = 0.05 (7 df), C₂ = 14.0671

If

Reject H₀

Test statistic is:

Since, 12.6 < 14.0671 DO NOT REJECT H₀

Must assume that the sample is drawn from N(m ,s ²).
Note that if a = 0.1 is used, we would reject H₀.

10.68 (a)

, where a= 0.05, a/2= 0.025, n = 10, m = 10

F_9,9,0.025 = 4.03 and 1/F_9,9,0.025 = 0.248

If

Reject H₀

Test statistic is:

Since, 0.248 < 1.03 < 4.03 DO NOT REJECT H₀

Note that the p value here is at least 0.2 because F_9,9,0.1 = 2.44

(b)

, with same a and F values

Test statistic is:

Since, 13.096 > 4.03 REJECT H₀

Note that the p value here must be less than 0.01 because F_9,9,0.005 = 6.54