Testing a Claim: Significance Test
Name ______________________________
A.
In the past, the mean score of the seniors at South High on the American College Testing
(ACT) college entrance examination has been 20. This year a special preparation course is
offered, and all 53 seniors planning to take the ACT test enroll in the course. The mean of their
53 ACT scores is 22.1. The principal believes that the new course has improved the students’
ACT scores. Assume that ACT scores for seniors at South High vary Normally with standard
deviation 6.
1. Identify the population and parameter of interest. State hypotheses in both words and
symbols for testing the principal’s claim.
2. Identify the appropriate statistical procedure and verify conditions for its use.
3. Calculate the test statistic and the P-value. Illustrate using the graph provided.
.50
-3.0
3 .0
-.50
4. State your conclusions clearly in complete sentences.
Inference Toolbox: Significance Test. (Chps. 11-15)
To test a claim about an unknown population parameter.
Step 1: Hypotheses, Identify the population of interest and the
parameter you draw conclusions about. State Hypotheses.
Step 2: Conditions, Choose the appropriate inference procedure.
Check for: SRS, Normality, Independence.
Step 3: Calculations, If conditions are met carry out the inference
procedure
 Calculate the test statistic.
 Find the P-value.
Step 4: Interpretation, Interpret your results in context of the
problem.
 Interpret the P-value or make a decision about H0 using
statistical significance.
 3 C’s: conclusion, connection, and context.
B… Here are the Degree of Reading Power (DRP) scores for an SRS of 44 third-grade students
from a suburban school district:
40
26
39
14
42
18
25
43
46
27
19
47
19
26
35
34
15
44
40
38
31
46
52
25
35
35
33
29
34
41
49
28
52
47
35
48
22
33
41
51
27
14
54
45
Suppose that the standard deviation of scores in this school district is known to be  = 11. The
researcher believes that the mean score  of all third-graders in this district is higher than the
national mean, which is 32. Carry out a significance test of the researcher’s belief at the
  0.05 significance level.
C. Here are measurements (in millimeters) of a critical dimension for a random sample of 16
auto engine crankshafts:
224.120
224.001
224.017
223.98
223.989 223.961 223.960
224.089
223.987
223.976
223.902
223.980 224.098 224.057
223.913
223.999
The data come from a production process that is known to have standard deviation  = 0.060
mm. The process mean is supposed to be  = 224 mm but can drift away from this target during
production. Is there sufficient evidence to conclude that the mean dimension is not 224 mm?
Give appropriate statistical evidence to support your conclusion.
D. Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults
can read four paragraphs of text in an average time of 22 seconds in the common Times New
Roman font. Ask 25 adults to read this text in the ornate font named Gigi. Here are their times:
23.2 21.2 28.9 27.7 29.1 27.3 16.1 22.6 25.6
34.2 23.9 26.8 20.5 34.3 21.4 32.6 26.2 34.1
31.5 24.6 23.0 28.6 24.4 28.1 41.3
Suppose that reading times are Normal with  = 6 seconds. Is there good evidence that the
mean reading time for Gigi is greater than 22 seconds? Carry out an appropriate test to help you
answer this question.