AP Statistics
Practice- Hypothesis Test and CI Practice #2
Two Populations
Name:____________________________________
Date:_____________________________________
1.
Two coins are flipped at random. Coin 1 is flipped 750 times with 379 tosses resulting in heads. Coin 2
is flipped 45 times with 22 tosses resulting in heads. Use a 0.10 significance level to test the claim that
there is no significant difference in population proportions of heads between the two sets.
2.
Cann’s Classes I:
Class A has 13 students. Class B has 36 students. Both classes took identical
tests on “Probability.” There were 5 passing papers in Class A and 23 passing papers in Class B. Use a
0.10 significance level to test the claim that there is no significant difference in population proportions
between the two classes. Construct a 90% confidence interval estimate of the true population proportion
difference.
3.
A group of 7 men were attempting to lose weight. They enroll in a program during which their diets are
strictly regulated. The men weigh in before beginning the program and then 30 days later. The results
are in the table below.
Weight 1
2
3
4
5
6
7
Before 216 195 200 160 201 153 247
After 204 193 187 158 181 151 225
At the 0.01 significance level, test the claim that the diet regulation was effective.
4.
Measures of the left- and right-hand gripping strengths of 10 left-handed writers are recorded:
Left
Hand
Right
Hand
1
140
2
90
3
125
4
129
5
95
Person
6
121
7
85
8
97
9
131
10
110
138
87
110
131
96
120
86
90
129
100
Test the claim that left-handed people have greater gripping strength in their left-hands as opposed to
their right hands. Construct a 99% confidence interval for the mean difference. What does your
confidence interval suggest about the equality of the two population means.
5.
Cann’s Classes II: Class A has 13 students. Class B has 36 students. Both classes took identical
tests on “Descriptive Statistics.” The mean and standard deviation for class A was 60 and 26.1
respectively. The mean and standard deviation for class B was 77 and 26.0 respectively. Use a 0.10
significance level to test the claim that there is no significant difference in population means between the
two classes. Construct a 90% confidence interval estimate of the true mean difference.
6.
The top 10 quarterbacks through week 12 in the NFL in the 2007-2008 season had a mean passing
yardage of 2781.313 and a standard deviation of 269.5404 yards. The top 5 quarterbacks through week
12 in the NFL in the 2008-2009 season have a mean passing yardage of 3084.4 and a standard deviation
of 297.356 yards. At the 0.05 significance level, test the claim that there was a significant increase in
passing yardage between the two seasons.
Statistics
PBLM SET- Hypothesis Test and CI Practice #2
Two Populations
Answer Key
Name:____________________________________
Date:_____________________________________
1.
COIN #1
COIN #2
H 0 : p1  p 2
n  750
x  379
n  45
x  22
H 1 : p1  p 2 Use stat test #6
P-value= 0.8303
  0.10
P  value    Don ' t reject H 0
There is insufficient evidence to reject the claim that the population proportion of heads is equal for the two
coins at the 0.10 significance level.
2.
A
B
H 1 : p1  p 2
n  13
x5
n  36
x  23
H 0 : p1  p 2
P-value= 0.112
Use stat test #6
  0.10
P  value    Don ' t reject H 0
There is insufficient evidence to reject the claim that there is no significant difference in population proportion
of passing papers between classes A and B at the 0.10 significance level.
CI= 90%
Use stat test #B
(-.5123, 0.00379)
We are 90% confident that the difference in population proportion of passing papers between the two classes
is between -51.23% & .379%.
3.
Input " before" in L1
Input " after" in L2
H 1 : 1   2
H 0 : 1   2
let : L3  L1  L2
Use stat calc 2: select data and let: “List:” be L3
P-value= 0.00937
P  value    reject H 0
There is sufficient evidence to reject the claim that the population mean weights before and after beginning the
program are equal at the 0.01 significance level. Therefore, the claim of effectiveness is true.
4.
*Think of as Matched Pairs*
Input " left" in L1
Input " right " in L2
Let  = 0.05
H 1 : 1   2
H 0 : 1   2
let : L3  L1  L2
Use stat calc 2: select data and let: “List:” be L3
P-value= 0.0334
P  value    reject H 0
There is sufficient evidence to reject the claim that there is no difference in population mean gripping
strengths between left-handed individuals’ left and right hands at the 0.05 significance level. Therefore,
the claim of left-handed people have greater gripping strength in their left-hands as opposed to their
right hands is true.
CI= 99%
Use stat test #8
(-2.012, 9.2122)
We are 99% confident that the difference in mean gripping strengths between the left and right hands of
lefties is between -2.012 and 9.2122.
The above confidence interval supports equality between the two means because 0 is in the set. When 0 is in a
confidence interval it shows that the difference between the two means is likely 0 which implies equality.
5.
x  60
B
x  77
s  26.1
s  26
n  13
n  36
A
H 1 : 1   2
H 0 : 1   2
Use stat test #4
  0.10
P-value= 0.0568
P  value    reject H 0
There is sufficient evidence to reject the claim that there is no difference in population mean scores between
class A and B at the 0.10 significance level. Therefore, the claim of a significant difference is true.
CI= 90%
Use stat test #0
(-31.51, -2.489)
We are 90% confident that the difference in population mean scores is between -31.51 & -2.489 pts.
6.
2007  2008
2008  2009
x  2781.313
x  3084.4
s  269.5404
s  297.356
n  10
n5
P-value= 0.0471
H 1 : 1   2
H 0 : 1   2
Use stat test #4
  0.05
P  value    reject H 0
There is sufficient evidence to reject the claim that the population mean passing yards between the 07/08 &
08/09 seasons are equal at the 0.05 significance level. Therefore, the claim of improvement is true.