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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,
Z0.005 = 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,
-Za= -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
Z0.005 = 2.58
Reject if 
Test statistic is: 
Since, 3.65> 2.58 REJECT H0
10.10 (a) 
, where
a = 0.01, Z0.01 = 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,
Za/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,
Z0.025 = 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,
Z0.005 = 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,
t0.025= 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
F9,9,0.025 = 4.03 and
1/F9,9,0.025 = 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 F9,9,0.1 = 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 F9,9,0.005 = 6.54