Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 8.5, Problem 46E
Refer to Example 8.4 and suppose that Y is a single observation from an exponential distribution with mean θ.
a Use the method of moment-generating
b Use the pivotal quantity 2Y/θ to derive a 90% confidence interval for θ.
c Compare the interval you obtained in part (b) with the interval obtained in Example 8.4.
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Students have asked these similar questions
Suppose a sample Y1, ..., Yn is selected from an exponential distribution with E (Yi) = θ and V (Yi) = θ2. Let θˆ be an estimator of the mean, θ.1. Explain what a parameter is. What is the parameter of interest in this case?2. Name the properties of a good estimator and explain, shortly, what is meant by each. (a)(b)
(c)3. Given the properties you discussed in (2) and the parameter of interest identified in (1), what estimator would you propose?4. What would the sampling distribution of this estimator be? Why?
question 3 and 4 please
We analyze a data set with Y = stopping distance of a car
and X = speed of the car when the brakes were applied,
%3D
and after running the data in STATISTICA, we obtain the
following results.
Std.Err.
of b
Std.Err.
of b*
t(61)
p-value
b*
N=63
Intercept
Speed
-20.2734
3.1366
-6.26038
20.67978
0.000000
0.000000
3.238368
0.935504
0.045238
0.151674
Sums of
df
Mean
p-value
Squares
Squares
59540.15
Effect
59540.15
427.6534
0.000000
Regress.
Residual
1
8492.74
61
139.23
Total
68032.89
Speed X StopDist Y Speed squared StopDist squared Speed StopDist
65853
Total
1195
2471
28719
164951
One of the observations is (X = 39, Y = 138).
The value of the internal studentized residual is
. (final answer to 2 decimal places e.g.
2.12)
Hence, the point (39, 138)
an outlier.
(choose from is or is not)
Chapter 8 Solutions
Mathematical Statistics with Applications
Ch. 8.2 - Using the identity ()=[E()]+[E()]=[E()]+B(), Show...Ch. 8.2 - a. If is an unbiased estimator for , what is B()?...Ch. 8.2 - Suppose that is an estimator for a parameter and...Ch. 8.2 - Refer to Exercise 8.1. a. If is an unbiased...Ch. 8.2 - Refer to Exercises 8.1 and consider the unbiased...Ch. 8.2 - Suppose that E(1)=E(2)=, V(1)=12, and V(2)=22....Ch. 8.2 - Consider the situation described in Exercise 8.6....Ch. 8.2 - Suppose that Y1, Y2, Y3 denote a random sample...Ch. 8.2 - Suppose that Y1, Y2,, Yn constitute a random...Ch. 8.2 - The number of breakdowns per week for a type of...
Ch. 8.2 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 8.2 - The reading on a voltage meter connected to a test...Ch. 8.2 - We have seen that if Y has a binomial distribution...Ch. 8.2 - Prob. 14ECh. 8.2 - Let Y, Y2,,Yn denote a random sample of size n...Ch. 8.2 - Suppose that Y1, Y2,,Yn constitute a random sample...Ch. 8.2 - If Y has a binomial distribution with parameters n...Ch. 8.2 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 8.2 - Prob. 19ECh. 8.2 - Suppose that Y1, Y2, Y3, Y4 denote a random sample...Ch. 8.4 - An investigator is interested in the possibility...Ch. 8.4 - An increase in the rate of consumer savings...Ch. 8.4 - The Environmental Protection Agency and the...Ch. 8.4 - A study was conducted to compare the mean number...Ch. 8.4 - The Mars twin rovers, Spirit and Opportunity,...Ch. 8.4 - A random sample of 985 likely votersthose who are...Ch. 8.4 - In a study of the relationship between birth order...Ch. 8.4 - Sometimes surveys provide interesting information...Ch. 8.4 - Refer to Exercise 8.29. Give the point estimate...Ch. 8.4 - In a study to compare the perceived effects of two...Ch. 8.4 - An auditor randomly samples 20 accounts receivable...Ch. 8.4 - Refer to Exercise 8.32. From the data given on the...Ch. 8.4 - We can place a 2-standard-deviation bound on the...Ch. 8.4 - Prob. 35ECh. 8.4 - Prob. 36ECh. 8.4 - Refer to Exercise 8.36. An engineer observes n =...Ch. 8.4 - Prob. 38ECh. 8.5 - Suppose that the random variable Y has a gamma...Ch. 8.5 - Suppose that the random variable Y is an...Ch. 8.5 - Suppose that Y is normally distributed with mean 0...Ch. 8.5 - Prob. 42ECh. 8.5 - Prob. 43ECh. 8.5 - Let Y have probability density function...Ch. 8.5 - Refer to Exercise 8.44. a Use the pivotal quantity...Ch. 8.5 - Refer to Example 8.4 and suppose that Y is a...Ch. 8.5 - Refer to Exercise 8.46. Assume that Y1, Y2, , Yn...Ch. 8.5 - Prob. 48ECh. 8.6 - Refer to Example 8.8. In this example, p1 and p2...Ch. 8.6 - Prob. 51ECh. 8.6 - Prob. 52ECh. 8.6 - Prob. 53ECh. 8.6 - Prob. 54ECh. 8.6 - Prob. 55ECh. 8.6 - Is Americas romance with movies on the wane? In a...Ch. 8.6 - Refer to Exercise 8.29. According to the result...Ch. 8.6 - The administrators for a hospital wished to...Ch. 8.6 - When it comes to advertising, tweens are not ready...Ch. 8.6 - What is the normal body temperature for healthy...Ch. 8.6 - A small amount of the trace element selenium, from...Ch. 8.6 - The following statistics are the result of an...Ch. 8.6 - Most Americans love participating in or at least...Ch. 8.6 - In a CNN/USA Today/Gallup Poll, 1000 Americans...Ch. 8.6 - For a comparison of the rates of defectives...Ch. 8.6 - Historically, biology has been taught through...Ch. 8.6 - One suggested method for solving the...Ch. 8.6 - Prob. 68ECh. 8.6 - Prob. 69ECh. 8.7 - Let Y be a binomial random variable with parameter...Ch. 8.7 - A state wildlife service wants to estimate the...Ch. 8.7 - Telephone pollsters often interview between 1000...Ch. 8.7 - Refer to Exercise 8.59. How many tweens should...Ch. 8.7 - Prob. 74ECh. 8.7 - Prob. 75ECh. 8.7 - Refer to the comparison of the daily adult intake...Ch. 8.7 - Prob. 77ECh. 8.7 - Refer to Exercise 8.65. How many items should be...Ch. 8.7 - Refer to Exercise 8.66. a Another similar study is...Ch. 8.8 - Although there are many treatments for bulimia...Ch. 8.8 - The carapace lengths of ten lobsters examined in a...Ch. 8.8 - Scholastic Assessment Test (SAT) scores, which...Ch. 8.8 - Chronic anterior compartment syndrome is a...Ch. 8.8 - Organic chemists often purify organic compounds by...Ch. 8.8 - Two new drugs were given to patients with...Ch. 8.8 - The Environmental Protection Agency (EPA) has...Ch. 8.8 - Refer to Exercise 8.88. Another common...Ch. 8.8 - Do SAT scores for high school students differ...Ch. 8.8 - Seasonal ranges (in hectares) for alligators were...Ch. 8.8 - Solid copper produced by sintering (heating...Ch. 8.8 - Prob. 93ECh. 8.8 - Suppose that we obtain independent samples of...Ch. 8.9 - The EPA has set a maximum noise level for heavy...Ch. 8.9 - In Exercise 8.81, we gave the carapace lengths of...Ch. 8.9 - Suppose that S2 is the sample variance based on a...Ch. 8.9 - Prob. 98ECh. 8.9 - Prob. 99ECh. 8.9 - Industrial light bulbs should have a mean life...Ch. 8.9 - In laboratory work, it is desirable to run careful...Ch. 8.9 - The ages of a random sample of live university...Ch. 8.9 - A precision instrument is guaranteed to read...Ch. 8 - Prob. 104SECh. 8 - Prob. 105SECh. 8 - In a controlled pollination study involving Phlox...Ch. 8 - Prob. 107SECh. 8 - Prob. 108SECh. 8 - To estimate the proportion of unemployed workers...Ch. 8 - Prob. 110SECh. 8 - Prob. 111SECh. 8 - Prob. 112SECh. 8 - Prob. 113SECh. 8 - Prob. 114SECh. 8 - Prob. 115SECh. 8 - Do we lose our memory capacity as we get older? In...Ch. 8 - Prob. 117SECh. 8 - Prob. 118SECh. 8 - Prob. 119SECh. 8 - Two methods for teaching reading were applied to...Ch. 8 - Prob. 121SECh. 8 - Prob. 122SECh. 8 - Prob. 123SECh. 8 - Prob. 124SECh. 8 - Prob. 125SECh. 8 - Prob. 126SECh. 8 - Prob. 127SECh. 8 - Prob. 128SECh. 8 - Prob. 129SECh. 8 - Prob. 130SECh. 8 - Refer to Exercises 1.129 and 1.130. S2 and S2 are...Ch. 8 - Prob. 132SECh. 8 - Prob. 133SECh. 8 - Prob. 134SECh. 8 - Prob. 135SECh. 8 - Prob. 136SE
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