Download Test 10A - Princeton High School

Test 10A
AP Statistics
Name:
Directions: Work on these sheets. Answer completely, but be concise. A normal probability table is
attached.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. You want to compute a 96% confidence interval for a population mean. Assume that the
population standard deviation is known to be 10 and the sample size is 50. The value of z* to be
used in this calculation is
(a) 1.960
(b) 1.645
(c) 1.7507
(d) 2.0537
(e) None of the above. The answer is
.
2. You want to estimate the mean SAT score for a population of students with a 90% confidence
interval. Assume that the population standard deviation is  = 100. If you want the margin of
error to be approximately 10, you will need a sample size of
(a) 16
(b) 271
(c) 38
(d) 1476
(e) None of the above. The answer is
.
3. A significance test gives a P-value of 0.04. From this we can
(a) Reject H0 at the 1% significance level
(b) Reject H0 at the 5% significance level
(c) Say that the probability that H0 is false is 0.04
(d) Say that the probability that H0 is true is 0.04
(e) None of the above. The answer is
.
4. A significance test was performed to test the null hypothesis H0: µ = 2 versus the alternative Ha:
µ  2. The test statistic is z = 1.40. The P-value for this test is approximately
(a) 0.16
(b) 0.08
(c) 0.003
(d) 0.92
(e) 0.70
(f) None of the above. The answer is
.
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Test 10A
5. You have measured the systolic blood pressure of a random sample of 25 employees of a
company located near you. A 95% confidence interval for the mean systolic blood pressure for the
employees of this company is (122, 138). Which of the following statements gives a valid
interpretation of this interval?
(a) Ninety-five percent of the sample of employees has a systolic blood pressure between 122 and
138.
(b) Ninety-five percent of the population of employees has a systolic blood pressure between 122
and 138.
(c) If the procedure were repeated many times, 95% of the resulting confidence intervals would
contain the population mean systolic blood pressure.
(d) The probability that the population mean blood pressure is between 122 and 138 is .95.
(e) If the procedure were repeated many times, 95% of the sample means would be between 122
and 138.
(f) None of the above. The answer is
.
6. An analyst, using a random sample of n = 500 families, obtained a 90% confidence interval for
mean monthly family income for a large population: ($600, $800). If the analyst had used a 99%
confidence coefficient instead, the confidence interval would be:
(a)
(b)
(c)
(d)
(e)
Narrower and would involve a larger risk of being incorrect
Wider and would involve a smaller risk of being incorrect
Narrower and would involve a smaller risk of being incorrect
Wider and would involve a larger risk of being incorrect
Wider but it cannot be determined whether the risk of being incorrect would be larger or
smaller
7. To determine the reliability of experts used in interpreting the results of polygraph examinations in
criminal investigations, 280 cases were studied. The results were:
Examiner’s
Decision
“Innocent”
“Guilty”
True Status
Innocent
Guilty
131
15
9
125
If the hypotheses were H0: suspect is innocent vs. Ha: suspect is guilty, then we could estimate the
probability of making a Type II error as:
(a) 15/280
(b) 9/280
(c) 15/140
(d) 9/140
(e) 15/146
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Test 10A
Part 2: Free Response
Communicate your thinking clearly and completely.
8. It is believed that the average amount of money spent per U.S. household per week on food is
about $98, with standard deviation $10. A random sample of 100 households in a certain affluent
community yields a mean weekly food budget of $100. We want to test the hypothesis that the
mean weekly food budget for all households in this community is higher than the national average.
(a) Perform a significance test at the   0.05 significance level. Follow the inference toolbox.
(b) Describe a Type I error in the context of this problem. What is the probability of making a
Type I error?
(c) Describe a Type II error in the context of this problem. Give two ways to reduce the probability
of a Type II error.
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Test 10A
9. There are many ways to measure the reading ability of children. Research designed to improve
reading performance is dependent on good measures of the outcome. One frequently used test is
the DRP or Degree of Reading Power. A researcher suspects that the mean score µ of all third
graders in Henrico County Schools is different from the national mean, which is 32. To test her
suspicion, she administers the DRP to an SRS of 44 Henrico County third-grade students. Their
scores were:
40
47
52
47
26
19
25
35
39
26
35
48
14
35
35
22
42
34
33
33
18
15
29
41
25
44
34
51
43
40
41
27
46
38
49
14
27
31
28
54
19
46
52
45
She then asked Minitab to calculate some descriptive statistics from this data set:
MTB > Describe 'DRPscore'.
DRPscore
N
44
MEAN
35.09
MEDIAN
35.00
TRMEAN
35.25
DRPscore
MIN
14.00
MAX
54.00
Q1
26.25
Q3
44.75
STDEV
11.19
SEMEAN
1.69
You may assume that DRP scores are approximately normal, and that the standard deviation of scores
in Henrico County Schools is known to be  = 11.
(a) Construct a 90% confidence interval for the mean DRP score in Henrico County Schools.
Follow the Inference Toolbox.
(b) Use the confidence interval you constructed in (a) to test the researcher’s claim. Be sure to state
your hypotheses and your significance level.
I pledge that I have neither given nor received aid on this test.__________________________
Chapter 10
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Test 10A