Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 10.2, Problem 5E
Let Y1 and Y2 be independent and identically distributed with a uniform distribution over the interval (θ, θ + 1). For testing H0: θ = 0 versus Ha: θ > 0, we have two competing tests:
Test 1: Reject H0 if Y1 > .95.
Test 2: Reject H0 if Y1 + Y2 > c.
Find the value of c so that test 2 has the same value for α as test 1. [Hint: In Example 6.3, we derived the density and distribution
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Students have asked these similar questions
I just need to know why this is wrong below:
What is the test statistic W? W=5 (incorrect)
and
What is the p-value of this test? (p-value < 0.001-- incorrect)
Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages
pages
127
217
486
132
397
297
396
327
292
256
358
272
What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12
Alpha Level
0.001
0.005
0.01
0.025
0.05
0.1
0.2
Critical Value
75
70
68
64
60
56
50
What is the p-value for this test? p-value < 0.001
ons
12. A sociologist hypothesizes that the crime rate is higher in areas
with higher poverty rate and lower median income. She col-
lects data on the crime rate (crimes per 100,000 residents),
the poverty rate (in %), and the median income (in $1,000s)
from 41 New England cities. A portion of the regression results
is shown in the following table.
Standard
Coefficients
error
t stat
p-value
Intercept
-301.62
549.71
-0.55 0.5864
Poverty
53.16
14.22
3.74 0.0006
Income
4.95
8.26
0.60 0.5526
a.
b.
Are the signs as expected on the slope coefficients?
Predict the crime rate in an area with a poverty rate of
20% and a median income of $50,000.
3. Using data from 50 work
2. The owner of several used-car dealerships believes that the
selling price of a used car can best be predicted using the car's
age. He uses data on the recent selling price (in $) and age of
20 used sedans to estimate Price = Po + B₁Age + ε. A portion
of the regression results is shown in the accompanying table.
Standard
Coefficients
Intercept
21187.94
Error
733.42
t Stat p-value
28.89 1.56E-16
Age
-1208.25
128.95 -9.37
2.41E-08
a. What is the estimate for B₁? Interpret this value.
b. What is the sample regression equation?
C. Predict the selling price of a 5-year-old sedan.
Chapter 10 Solutions
Mathematical Statistics with Applications
Ch. 10.2 - Define and for a statistical test of hypotheses.Ch. 10.2 - An experimenter has prepared a drug dosage level...Ch. 10.2 - Refer to Exercise 10.2. a Find the rejection...Ch. 10.2 - Suppose that we wish to test the null hypothesis...Ch. 10.2 - Let Y1 and Y2 be independent and identically...Ch. 10.2 - We are interested in testing whether or not a coin...Ch. 10.2 - True or False Refer to Exercise 10.6. a The level...Ch. 10.2 - A two-stage clinical trial is planned for testing...Ch. 10.3 - A survey published in the American Journal of...Ch. 10.3 - The hourly wages in a particular industry are...
Ch. 10.3 - The output voltage for an electric circuit is...Ch. 10.3 - The Rockwell hardness index for steel is...Ch. 10.3 - Shear strength measurements derived from...Ch. 10.3 - Prob. 22ECh. 10.3 - Studies of the habits of white-tailed deer...Ch. 10.3 - A study by Childrens Hospital in Boston indicates...Ch. 10.3 - An article in American Demographics reports that...Ch. 10.3 - According to the Washington Post, nearly 45% of...Ch. 10.3 - The state of California is working very hard to...Ch. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - In March 2001, a Gallup poll asked. How would you...Ch. 10.3 - A political researcher believes that the fraction...Ch. 10.3 - Exercise 8.58 stated that a random sample of 500...Ch. 10.3 - Michael Sosin investigated determinants that...Ch. 10.3 - Prob. 36ECh. 10.4 - Refer to Exercise 10.19. If the voltage falls as...Ch. 10.4 - Refer to Exercise 10.20. The steel is sufficiently...Ch. 10.4 - Refer to Exercise 10.30. Calculate the value of ...Ch. 10.4 - Refer to Exercise 10.33. The political researcher...Ch. 10.4 - Refer to Exercise 10.34. Using the rejection...Ch. 10.4 - In Exercises 10.34 and 10.41, how large should the...Ch. 10.4 - A random sample of 37 second graders who...Ch. 10.4 - Refer to Exercise 10.43. Find the sample sizes...Ch. 10.5 - Refer to Exercise 10.21. Construct a 99%...Ch. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.6 - High airline occupancy rates on scheduled flights...Ch. 10.6 - Two sets of elementary schoolchildren were taught...Ch. 10.6 - A biologist has hypothesized that high...Ch. 10.6 - How would you like to live to be 200 years old?...Ch. 10.6 - Do you believe that an exceptionally high...Ch. 10.6 - A check-cashing service found that approximately...Ch. 10.6 - Prob. 56ECh. 10.6 - Prob. 57ECh. 10.6 - Prob. 58ECh. 10.8 - Why is the Z test usually inappropriate as a test...Ch. 10.8 - Prob. 62ECh. 10.8 - A chemical process has produced, on the average,...Ch. 10.8 - A coin-operated soft-drink machine was designed to...Ch. 10.8 - Operators of gasoline-fueled vehicles complain...Ch. 10.8 - Researchers have shown that cigarette smoking has...Ch. 10.8 - Nutritional information provided by Kentucky Fried...Ch. 10.8 - Prob. 68ECh. 10.8 - Two methods for teaching reading were applied to...Ch. 10.8 - A study was conducted by the Florida Game and Fish...Ch. 10.8 - Under normal conditions, is the average body...Ch. 10.8 - Prob. 72ECh. 10.8 - In Exercise 8.83, we presented some data collected...Ch. 10.8 - Prob. 74ECh. 10.8 - Prob. 75ECh. 10.8 - Prob. 76ECh. 10.8 - Prob. 77ECh. 10.9 - A manufacturer of hard safety hats for...Ch. 10.9 - Prob. 79ECh. 10.9 - Prob. 80ECh. 10.9 - Prob. 81ECh. 10.9 - Exercises 8.83 and 10.73 presented some data...Ch. 10.9 - Prob. 83ECh. 10.9 - An experiment published in The American Biology...Ch. 10.9 - Prob. 85ECh. 10.9 - Aptitude tests should produce scores with a large...Ch. 10.9 - Prob. 87ECh. 10.10 - Refer to Exercise 10.2. Find the power of the test...Ch. 10.10 - Prob. 89ECh. 10.10 - Refer to Exercise 10.5. a Find the power of test 2...Ch. 10.10 - Let Y1, Y2,, Y20 be a random sample of size n = 20...Ch. 10.10 - Consider the situation described in Exercise...Ch. 10.10 - For a normal distribution with mean and variance...Ch. 10.10 - Suppose that Y1, Y2, ,Yn constitute a random...Ch. 10.10 - Prob. 95ECh. 10.10 - Prob. 96ECh. 10.10 - Prob. 97ECh. 10.10 - Prob. 98ECh. 10.10 - Prob. 99ECh. 10.10 - Prob. 100ECh. 10.10 - Prob. 101ECh. 10.10 - Prob. 102ECh. 10.10 - Prob. 103ECh. 10.10 - Refer to the random sample of Exercise 10.103. a...Ch. 10.11 - Let Y1, Y2,, Yn denote a random sample from a...Ch. 10.11 - A survey of voter sentiment was conducted in four...Ch. 10.11 - Prob. 107ECh. 10.11 - Prob. 108ECh. 10.11 - Let X1, X2,, Xm denote a random sample from the...Ch. 10.11 - Show that a likelihood ratio test depends on the...Ch. 10.11 - Suppose that we are interested in testing the...Ch. 10.11 - Prob. 112ECh. 10.11 - Refer to Exercise 10.112. Show that in testing of...Ch. 10.11 - Prob. 114ECh. 10 - True or False. a If the p-value for a test is...Ch. 10 - Prob. 116SECh. 10 - Prob. 117SECh. 10 - Prob. 118SECh. 10 - Prob. 119SECh. 10 - Prob. 120SECh. 10 - Prob. 121SECh. 10 - Prob. 122SECh. 10 - A pharmaceutical manufacturer purchases a...Ch. 10 - Prob. 124SECh. 10 - Prob. 125SECh. 10 - Prob. 126SECh. 10 - Prob. 127SECh. 10 - Prob. 128SECh. 10 - Prob. 129SECh. 10 - Prob. 130SE
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