Statistical Reasoning for Everyday Life (5th Edition)
5th Edition
ISBN: 9780134494043
Author: Jeff Bennett, William L. Briggs, Mario F. Triola
Publisher: PEARSON
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Chapter 9.2, Problem 49E
To determine
Explain the meaning of type I and type II errors.
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Table 5: Measurement Data for Question 9
Part Number
Op-1, M-1
Op-1, M-2 | Op-2, M-1 Op-2, M-2 | Op-3, M-1
Op-3, M-2
1
21
20
20
20
19
21
2
24
23
24
24
23
24
3
4
5
6
7
8
9
10
11
21
12
8222332
201
21
20
22
20
22
27
27
28
26
27
28
19
18
19
21
24
21
22
19
17
18
24
23
25
25
23
26
20
20
18
19
17
13
23
25
25
2 3 3 3 3 2 3
18
18
21
21
23
22
24
22
20
19
23
24
25
24
20
21
19
18
25
25
14
24
24
23
25
24
15
29
30
30
28
31
16
26
26
25
26
25
17
20
20
19
20
20
843882388
20
18
25
20
19
25
25
30
27
20
18
19
21
19
19
21
23
19
25
26
25
24
25
25
20
19
19
18
17
19
17
Question 9
A measurement systems experiment involving 20 parts, three operators (Op-1, Op-2, Op-3), and two measure-
ments (M-1, M-2) per part is shown in Table 5.
(a) Estimate the repeatability and reproducibility of the gauge.
(b) What is the estimate of total gauge variability?"
(c) If the product specifications are at LSL = 6 and USL 60, what can you say about gauge capability?
Question 5
A fraction nonconforming control chart with center line 0.10, UCL = 0.19, and LCL = 0.01 is used to control a
process.
(a) If three-sigma limits are used, find the sample size for the control charte
2
(b) Use the Poisson approximation to the binomial to find the probability of type I error.
(c) Use the Poisson approximation to the binomial to find the probability of type II error if the process fraction
defective is actually p = 0.20.
Question 8
Ten parts are measured three times by the same operator in a gauge capability study. The data are shown in
Table 4.
(a) Describe the measurement error that results from the use of this gauge. I
(b) Estimate total variability and product variability.
(c) What percentage of total variability is due to the gauge?
(d) If specifications on the part are at 100±15, find the P/T ratio for this gauge. Comment on the adequacy
of the gauge.
3
Table 4: Measurement Data for Question 8
Part Number Measurement 1 Measurement 2 Measurement 3
1
2
100
95
101
100
93
97
3
101
103
100
4
96
95
97
5
98
98
96
6
99
98
98
7889
95
97
98
100
99
98
100
100
97
10
100
98
98
99
Chapter 9 Solutions
Statistical Reasoning for Everyday Life (5th Edition)
Ch. 9.1 - Hypotheses and Hypothesis Tests. What is a...Ch. 9.1 - Null and Alternative Hypotheses. What is a mill...Ch. 9.1 - Hypothesis Test Outcomes. What are the two...Ch. 9.1 - P-Value. What is a P-value for a hypothesis?Ch. 9.1 - Does It Make Sense? For Exercises 512, determine...Ch. 9.1 - Does It Make Sense? For Exercises 512, determine...Ch. 9.1 - Significance. The results of my hypothesis test...Ch. 9.1 - Does It Make Sense? For Exercises 512, determine...Ch. 9.1 - Does It Make Sense? For Exercises 512, determine...Ch. 9.1 - Does It Make Sense? For Exercises 512, determine...
Ch. 9.1 - Prob. 11ECh. 9.1 - Does It Make Sense? For Exercises 512, determine...Ch. 9.1 - What Is Significant? In testing a method of gender...Ch. 9.1 - What Is Significant? In testing a method of gender...Ch. 9.1 - Formulating Hypotheses. In Exercises 1522, state...Ch. 9.1 - Formulating Hypotheses. In Exercises 1522, state...Ch. 9.1 - Formulating Hypotheses. In Exercises 1522, state...Ch. 9.1 - Formulating Hypotheses. In Exercises 1522, state...Ch. 9.1 - Prob. 19ECh. 9.1 - Formulating Hypotheses. In Exercises 1522, state...Ch. 9.1 - Formulating Hypotheses. In Exercises 1522, state...Ch. 9.1 - Formulating Hypotheses. In Exercises 1522, state...Ch. 9.1 - Drawing a Conclusion from a Hypothesis Test. If we...Ch. 9.1 - Drawing a Conclusion from a Hypothesis Test. If we...Ch. 9.1 - Drawing a Conclusion from a Hypothesis Test. If we...Ch. 9.1 - Drawing a Conclusion from a Hypothesis Test. If we...Ch. 9.1 - Drawing a Conclusion from a Hypothesis Test. If we...Ch. 9.1 - Drawing a Conclusion from a Hypothesis Test. If we...Ch. 9.2 - Notation. Briefly describe what each of the...Ch. 9.2 - Standard Score. When testing a claim about a...Ch. 9.2 - Critical Values. What do we mean by critical...Ch. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Does It Make Sense? For Exercises 512, determine...Ch. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Using Critical Values to Reject or Not Reject. In...Ch. 9.2 - Using Critical Values to Reject or Not Reject. In...Ch. 9.2 - Using Critical Values to Reject or Not Reject. In...Ch. 9.2 - Using Critical Values to Reject or Not Reject. In...Ch. 9.2 - Using Critical Values to Reject or Not Reject. In...Ch. 9.2 - Using Critical Values to Reject or Not Reject. In...Ch. 9.2 - Using Critical Values to Reject or Not Reject. In...Ch. 9.2 - Using Critical Values to Reject or Not Reject. In...Ch. 9.2 - Using P-Values to Reject or Not Reject. In...Ch. 9.2 - Using P-Values to Reject or Not Reject. In...Ch. 9.2 - Using P-Values to Reject or Not Reject. In...Ch. 9.2 - Using P-Values to Reject or Not Reject. In...Ch. 9.2 - Using P-Values to Reject or Not Reject. In...Ch. 9.2 - Using P-Values to Reject or Not Reject. In...Ch. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Using P-Values to Reject or Not Reject. In...Ch. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Hypothesis Tests for Means. For Exercises 3548,...Ch. 9.2 - Hypothesis Tests for Means. For Exercises 3548,...Ch. 9.2 - Hypothesis Tests for Means. For Exercises 3548,...Ch. 9.2 - Prob. 38ECh. 9.2 - Hypothesis Tests for Means. For Exercises 3548,...Ch. 9.2 - Hypothesis Tests for Means. For Exercises 3548,...Ch. 9.2 - Prob. 41ECh. 9.2 - Hypothesis Tests for Means. For Exercises 3548,...Ch. 9.2 - Hypothesis Tests for Means. For Exercises 3548,...Ch. 9.2 - Prob. 44ECh. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - Prob. 49ECh. 9.2 - Type I and Type II Errors. In Exercises 4952, a...Ch. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.3 - Notation. What do n, p, p, and P-value represent?Ch. 9.3 - Standard Score. When testing a claim about a...Ch. 9.3 - Prob. 3ECh. 9.3 - P-Value. A P-value of 0.00001 is obtained when...Ch. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Does It Make Sense? For Exercises 59, determine...Ch. 9.3 - Prob. 9ECh. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9.3 - Prob. 11ECh. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9.3 - Hypothesis Tests for Population Proportions. For...Ch. 9 - A random sample of 40 quarters minted after 1964...Ch. 9 - In a study of smokers who tried to quit smoking...Ch. 9 - Finding a Job Through Networking. In a survey of...Ch. 9 - A medical student wants to test the claim that...Ch. 9 - Identify the null and alternative hypotheses for...Ch. 9 - Identify the null and alternate hypotheses for...Ch. 9 - Identify the null and alternative hypotheses for...Ch. 9 - Prob. 4CQCh. 9 - Prob. 5CQCh. 9 - Prob. 6CQCh. 9 - In Exercises 510, assume that we want to use a...Ch. 9 - Prob. 8CQCh. 9 - In Exercises 510, assume that we want to use a...Ch. 9 - Prob. 10CQ
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