GBS 221
Review for Exam 3
1.
The Colonial Canning Company of Claremont, California uses a machine to fill its
18-ounce cans of kumquats.
If the machine performs improperly, it is
readjusted.
A sample of 50 cans is found to have a mean of 18.9 ounces. The
population is known to have a standard deviation of 4.7 ounces. Test at the 95%
confidence level.
a. Perform a
hypothesis test to determine if the machine should be
readjusted.
Show all steps for full credit.
Ho:
μ = 18
Ha: μ ≠ 18
Z= 1.96 * ((18.9 – 18) / (4.7 /
√50))
Z= 1.354
=.9115
.9115 < .95
Do not reject, do not readjust
n
σ/
μ
x
z
0
b.
If the sample was 500 cans, yielding the same mean, should the machine be
readjusted?
Z = 1.96 * ((18.9 – 18) / (4.7 /
√500)
Z = 4.28
4.28 > 1.96
Reject, Readjust the machine

2.
A student believes that no more than 20% of the students who finish a
statistics course get an A.
A random sample of 100 students was taken.
Twenty-four percent of the students in the sample received A’s.
a.
State the null and alternative hypotheses.
n=100
Ho : P
≤ .24
Ha: P > .24
b.
Using a critical value, test the hypothesis at the 1% level of
significance.
Z= .24 - .2 /
√((.2(1-.2) / 100))
Z= 1
Do not reject Ho, 1 < 2.33, there is not sufficient evidence at a=1%
to conclude that more than 20% of the students get an A.
c.
Using a
p
-value, test the hypothesis at the 1% level of significance.
Critical value of Z=1
=.8413
since Left tail test
1 - .8413 = 0.1587
(same conclusion as part b)
3. The following sample information is given concerning the ACT scores of
high school seniors form two local schools.
School A
School B

1
n
=
14
2
n
=
15
1
x
= 25
2
x
= 23
2
1
= 16
2
2
= 10
Develop a 95% confidence interval estimate for the difference between
the two populations.
n
σ
+
n
σ
=
σ
2
2
2
1
2
1
X
2
X
1
Since the standard deviation is already squared making it variance
there is no need to square in function
25 – 23
±
1.96 *
√((16/14) + (10/15))
2
±
2.6366
-0.637 to 4.637
the results prove two tail test by one interval being negative and
one interval being positive.

4.
A poll was taken this year asking college students if they considered
themselves overweight.
A similar poll was taken five ago.
Results are
summarized below.
Use a hypothesis test to test if the proportion has
increased
significantly?
Let
= 0.05.
Sample Size
Number Considered
Themselves
Overweight
Current Sample
(c)
300
150
Previous Sample
(p)
275
121
Question asks for the proportion, a big hint showing this is
going to be a proportion hypothesis test. Asking increased
significantly means
Ho: Pc – Pp
≤ 0
Ha: Pc – Pp > 0
Use calculator for this problem
Steps:
Stat
Test
2-propZtest
Z=1.44
P-Value=.0749
.05 < .0749
Do not reject Ho

5. To catch more criminals, the governor has budgeted more money to put
more police on our city streets.
The decision was based on the following
data:
# of Police:
13
15
23
25
15
10
9
20
# Arrests:
8
9
12
18
8
6
5
10
a.

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- Fall '14
- Statistics, SOLUTIONS, Formulas, Probability, Sample, Answers , Proportion, Statistical hypothesis testing, critical value, Zchart