Hypothesis Tests for a Single Population Mean or Two Population Means
1. Find the P-value for each of the following hypothesis tests and state the conclusion at the  =
0.05 level.
(a) H0: µ = 100
Ha: µ > 100
Test Stat: t = 2.18 where n = 15
(b) H0: µ = 85.6
Ha: µ ¹ 85.6
Test Stat: t = 2.075 where n = 20
(c) H0: µ1 = µ2
Ha: µ1 < µ2
Test Stat: t = -1.46 where df = 64.07
2. The demographics of television viewers are an important factor in selling advertising time. The
RX pharmaceutical company would like to market a new acid-reflux medication to consumers
under the age of 50. They are considering buying advertising time on the cable channel MSNBC,
if they find evidence that the average age of MSNBC viewers is under 50 years. In a random
sample of 64 MSNBC viewers, the average age was 46.4 years with a standard deviation of 10
years. Based on this data, will the company purchase advertising time on MSNBC? Test the
relevant hypotheses at the  = 0.05 level. Do this first using the formulas and showing all work,
then by using the calculator. Finally, test the hypotheses with a 96% CI.
3. Researchers at Rochester Institute of Technology investigated the use of isolation time-out with
155 emotionally disturbed students enrolled in a special education facility (Exceptional
Children, Feb., 1995). The students were randomly assigned to one of two types of classrooms:
Type A classrooms (with a maximum of 12 students) and Type B classrooms (with a maximum
of 6 students). Over the academic year the number of incidents resulting in an isolation timeout was recorded for each student. Summary statistics for the two groups are shown in the
following table. Does the data suggest that the average number of timeouts in all Type A
classrooms is lower than the average number of all timeouts in Type B classrooms? Test the
relevant hypotheses at the  = 0.05 level.
Classroom
# of Students
Mean # Timeouts
Std Dev
Type A
100
78.67
59.08
Type B
55
102.87
69.33
4. According to WebMD (www.webmd.com), “normal” body temperature is an average. Not only
is body temperature different for different people, it also changes during the day and is very
sensitive to hormone levels. The table below summarizes body temperature data from the
Journal of Statistics Education Data Archive (Shoemaker, 1996).
Body Temperature (F)
Gender
n
Mean
StDev
Male
65
98.105
0.699
Female
65
98.394
0.743
Does the data suggest that there a significant difference in average body temperature for men
and women? Perform a hypothesis test at the  = 0.05 level to answer this question.
Solutions
1. (a) tcdf 2.18, ¥, 14 = 0.0234, Reject H0
(
)
(
)
(b) 2*tcdf 2.075, ¥, 19 = 0.0518, Fail to Reject H0
(
)
(c) tcdf -¥, -1.46, 64.07 = 0.0746, Fail to Reject H0
2. “BY HAND”
46.4 -50
t=
= -2.88
10
64
(
)
P-Value = tcdf -¥, -2.88, 63 = 0.0027
VIA THE CALCULATOR:
Run TTest with 0 = 50, x = 46.4, s = 10, n = 64 and “<” for the alternative
CI APPROACH:
Run TInterval via “Stats” x = 46.4, s = 10, n = 64 and C-Level = 0.96
WRITING UP THE TEST
H0:  = 50
Ha:  < 50
Test Stat: t = -2.88
P – Value = 0.0027
Conclusion: Reject H0: Our data supports that the average age of viewers of MSNBC is less than
50 years of age, and so the company should purchase advertising time.
Validity: n = 64 which is larger than 30
-orH0:  = 50
Ha:  < 50
(
)
96% CI = 43.779, 49.021
Conclusion: Reject H0: Our data supports that the average age of viewers of MSNBC is less than
50 years of age, and so the company should purchase advertising time.
Validity: n = 64 which is larger than 30
3.
Run the 2-SampTTest using “Stats” with the alternative “<” and:
x1 = 78.67
Sx1 = 59.08
n1 = 100
x 2 = 102.87
Sx 2 = 69.33
n2 = 55
H0: A = B
Ha: A < B
Test Stat: t = -2.188
P-Value = 0.0155
Conclusion: Reject H0: Our data supports that the mean number of timeouts in a type A
classroom will be less than that of a type B classroom.
Validity: Both samples sizes are at least 30.
4.
Run the 2-SampTTest using “Stats” with the alternative “ ¹” and:
x1 = 98.105
Sx1 = 0.699
n1 = 65
x 2 = 98.394
Sx 2 = 0.743
n2 = 65
H0: M = F
Ha: M
¹ F
Test Stat: t = -2.284
P-Value = 0.024
Conclusion: Reject H0: Our data supports that there is a significant difference in the average
body temperature between males and females.
Validity: Both samples sizes are at least 30.