For each problem, provide the hypotheses and test the hypotheses by calculating the test statistic
and p-value. Fill in all the blanks in the following sentence. Also, give calculator answer in
parentheses for the test statistic and p-value. This will not be corrected or graded but will help
prepare you for the exam.
1. A student read that in the bay area of California, the average person produces 2 pounds of
garbage per day. The student believed that she produced less than that but wanted to test her
hypothesis statistically. She collected data on 10 randomly selected days. Use  = 0.05.
2.0
2.3
1.9
1.9
2.3
1.2
2.3
2.1
1.7
1.8
H0:__µ=2____ H1:___ µ<2_____
What is the sample mean?
Sample Mean _____1.95___
What is the sample standard deviation?
t
x
s
t
n
______________
Formula
1.95  2
0.34075
10
________________
Substitution
Sample Standard Deviation___0.34075__
t = -0.4640
________________
Test Statistic value
____t = -0.4640__
Test Statistic value
Calculator:
p>0.25
________________
p-value
__p = 0.3268__
p-value
The average amount of garbage produced daily by the student ___is not___ significantly less
than 2 pounds (t = _-0.4640_, p = _0.3268___, n=__10__).
2. A living wage is the hourly rate that an individual must earn to support their family, if they
are the sole provider and are working full-time. In 2005, it was estimated that 33% of the job
openings had wages that were inadequate (below the living wage). A researcher wishes to
determine if that is still the case during this recession. In a sample of 460 jobs, 207 had wages
that were inadequate. Test the claim that the proportion of jobs with inadequate wages is greater
than 0.33. Let α = 0.01.
H0___p =0.33 _
H1_____p>0.33_____
pˆ  p
z = 5.47
p<0.0002
z
0.45  0.33
z
p1  p 
0.331  0.33
n
460
______________
Formula
Calculator:
________________
Substitution
________________
________________
Test Statistic value
p-value
___z = 5.47___
____2.21 x 10-8_____
Test Statistic value
p-value
3. Suppose you had two different ways to get to school. One way was on main roads with a lot
of traffic lights, the other way was on back roads with few traffic lights. You would like to know
which way is faster. You randomly select 6 days to use the main road and 6 days to use the back
roads. Your objective is to determine if the mean time it takes on the back road µb is different
than the mean time on the main road µm. The data is presented in the table below. The units are
minutes. Assume population variances are equal. Because the sample size is small, you decide to
use a significance level of α = 0.1.
Back Road 14.5
15.0
16.2
18.9
21.3
17.4
Main Road
19.5
17.3
21.2
20.9
Write the appropriate null and alternate hypotheses: H0: __µb=µm
21.1
17.7
H1:___ µb≠µm ___
What is the sample mean for each route?
Back Road___17.21__ Main Road __19.62
What is the sample standard deviation for each route?
Back Road__2.56___ Main Road __1.76
t
x A  x B    A   B 
 n A  1s A2  n B  1s B2   1


n A  nB  2
1 



  n A n B 
t
17.21  19.62  0
=-1.90
2
2
 6  12.56  6  11.76   1 1 



662

  6
6 
P<0.1
________________
________________
Test Statistic value
p-value
____-1.89____
_____0.0878______
Calculator:
Test Statistic value
p-value
There __is __ a significant difference between taking the back road and the main road (t =
_-1.89_, p = _0.0878___, n=__12__).
______________
Formula
________________
Substitution
4. Some parents of age group athletes believe their child will be better if they pay them a
financial reward for being successful. For example they may pay $5 for scoring a goal in soccer
or $1 for a best time at a swim meet. The argument against paying is that it is counterproductive
and destroys the child’s self-motivation. Is the dropout rate of children that have been paid
different than of children who have not been paid? Let α = 0.05.
Dropout rate of children who have been paid: 450 out of 510
Dropout rate of children who have not been paid: 780 out of 930
pˆ c 
H0___PA = PB____H1____ PA ≠ PB ____
x A  xB 450  780

 0.854
n A  nB 510  930
z
 pˆ A  pˆ B    p A  p B  z 
 1
1 

pˆ c 1  pˆ c 

 nA
______________
Formula
Calculator:
nB 
0.882  0.839  0
1 
 1
0.8541  0.854


 510 930 
________________
Substitution
z=2.21
________________
Test Statistic value
p=0.0272
________________
p-value
____z=2.24___
___p=0.0248_______
Test Statistic value
p-value