PROBABILITY & STATS FOR ENGINEERING &SCI
9th Edition
ISBN: 9781285099804
Author: DEVORE
Publisher: CENGAGE L
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Chapter 6.1, Problem 9E
Each of 150 newly manufactured items is examined and the number of scratches per item is recorded (the items are supposed to be free of scratches), yielding the following data:
| Number of scratches per item | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Observed frequency | 18 | 37 | 42 | 30 | 13 | 7 | 2 | 1 |
Let X = the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter μ.
- a. Find an unbiased estimator of p and compute the estimate for the data. [Hint: E(X) = μ for X Poisson, so E(X) = ?]
- b. What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint:
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Question 2
The data below provides the battery life of thirty eight (38) motorcycle batteries.
100 83 83 105 110 81 114
99 101 105 78 115 74 96
106
89
94 81 106 91 93 86
79 103 94 108 113 100
117 120
77 93
93 85 76
89 78 88
680
a. Test the hypothesis that mean battery life is greater than 90. Use the 1% level of
significance.
b. Determine if the mean battery life is different from 80. Use the 10% level of
significance. Show all steps for the hypothesis test
c. Would your conlcusion in part (b) change at the 5% level of significance? |
d. Confirm test results in part (b) using JASP. Note: All JASP input files and output
tables should be provided
Suppose that 80% of athletes at a certain college graduate. You randomly select eight athletes. What’s the chance that at most 7 of them graduate?
Suppose that you flip a fair coin four times. What’s the chance of getting at least one head?
Chapter 6 Solutions
PROBABILITY & STATS FOR ENGINEERING &SCI
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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