Probability and Statistics for Engineering and the Sciences STAT 400 - University Of Maryland
9th Edition
ISBN: 9781305764477
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 6.1, Problem 2E
The National Health and Nutrition Examination Survey (NHANES) collects demographic, socioeconomic, dietary, and health-related information on an annual basis. Here is a sample of 20 observations on HDL cholesterol level (mg/dl) obtained from the 2009-2010 survey (HDL is “good” cholesterol; the higher its value, the lower the risk for heart disease):
- a. Calculate a point estimate of the population mean HDL cholesterol level.
- b. Making no assumptions about the shape of the population distribution, calculate a point estimate of the value that separates the largest 50% of HDL levels from the smallest 50%.
- c. Calculate a point estimate of the population standard deviation.
- d. An HDL level of at least 60 is considered desirable as it corresponds to a significantly lower risk of heart disease. Making no assumptions about the shape of the population distribution, estimate the proportion p of the population having an HDL level of at least 60.
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Microsoft Excel include formulas
Question 1
The data shown in Table 1 are and R values for 24 samples of size n = 5 taken from a process producing
bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals
recorded (i.e., 34.5 should be 0.50345).
Table 1: Bearing Diameter Data
Sample Number
I
R
Sample Number
I R
1
34.5
3
13
35.4
8
2
34.2
4
14
34.0
6
3
31.6
4
15
37.1
5
4
31.5
4
16
34.9
7
5
35.0
5
17
33.5
4
6
34.1
6
18
31.7
3
7
32.6
4
19
34.0
8
8
33.8
3
20
35.1
9
34.8
7
21
33.7
2
10
33.6
8
22
32.8
1
11
31.9
3
23
33.5
3
12
38.6 9
24
34.2
2
(a) Set up and R charts on this process. Does the process seem to be in statistical control? If necessary,
revise the trial control limits. [15 pts]
(b) If specifications on this diameter are 0.5030±0.0010, find the percentage of nonconforming bearings pro-
duced by this process. Assume that diameter is normally distributed. [10 pts]
1
4. (5 pts) Conduct a chi-square contingency test (test of independence) to assess whether
there is an association between the behavior of the elderly person (did not stop to talk,
did stop to talk) and their likelihood of falling. Below, please state your null and
alternative hypotheses, calculate your expected values and write them in the table,
compute the test statistic, test the null by comparing your test statistic to the critical
value in Table A (p. 713-714) of your textbook and/or estimating the P-value, and
provide your conclusions in written form. Make sure to show your work.
Did not stop walking to talk
Stopped walking to talk
Suffered a fall
12
11
Totals
23
Did not suffer a fall | 2
Totals
35
37
14
46
60
T
Chapter 6 Solutions
Probability and Statistics for Engineering and the Sciences STAT 400 - University Of Maryland
Ch. 6.1 - The accompanying data on flexural strength (MPa)...Ch. 6.1 - The National Health and Nutrition Examination...Ch. 6.1 - Consider the following sample of observations on...Ch. 6.1 - The article from which the data in Exercise 1 was...Ch. 6.1 - As an example of a situation in which several...Ch. 6.1 - Urinary angiotensinogen (AGT) level is one...Ch. 6.1 - a. A random sample of 10 houses in a particular...Ch. 6.1 - In a random sample of 80 components of a certain...Ch. 6.1 - Each of 150 newly manufactured items is examined...Ch. 6.1 - Using a long rod that has length , you are going...
Ch. 6.1 - Of n1 randomly selected male smokers, X1 smoked...Ch. 6.1 - Suppose a certain type of fertilizer has an...Ch. 6.1 - Consider a random sample X1,..., Xn from the pdf...Ch. 6.1 - A sample of n captured Pandemonium jet fighters...Ch. 6.1 - Let X1, X2,..., Xn represent a random sample from...Ch. 6.1 - Suppose the true average growth of one type of...Ch. 6.1 - In Chapter 3, we defined a negative binomial rv as...Ch. 6.1 - Let X1, X2,..., Xn be a random sample from a pdf...Ch. 6.1 - An investigator wishes to estimate the proportion...Ch. 6.2 - A diagnostic test for a certain disease is applied...Ch. 6.2 - Let X have a Weibull distribution with parameters ...Ch. 6.2 - Let X denote the proportion of allotted time that...Ch. 6.2 - Let X represent the error in making a measurement...Ch. 6.2 - A vehicle with a particular defect in its emission...Ch. 6.2 - The shear strength of each of ten test spot welds...Ch. 6.2 - Consider randomly selecting n segments of pipe and...Ch. 6.2 - Let X1,..., Xn be a random sample from a gamma...Ch. 6.2 - Prob. 28ECh. 6.2 - Consider a random sample X1, X2,, Xn from the...Ch. 6.2 - At time t = 0, 20 identical components are tested....Ch. 6 - An estimator is said to be consistent if for any ...Ch. 6 - a. Let X1,.., Xn be a random sample from a uniform...Ch. 6 - At time t = 0, there is one individual alive in a...Ch. 6 - The mean squared error of an estimator is MSE ()...Ch. 6 - Prob. 35SECh. 6 - When the population distribution is normal, the...Ch. 6 - When the sample standard deviation S is based on a...Ch. 6 - Each of n specimens is to be weighed twice on the...
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