Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 8.4, Problem 21E
An investigator is interested in the possibility of merging the capabilities of television and the Internet. A random sample of n = 50 Internet users yielded that the
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Microsoft Excel snapshot for random sampling: Also note the formula used for the last
column
02
x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
A
B
1
No.
States
2
1
ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
B
E
F
G
1
No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
sample
10
3
2 ALASKA
0.4493186 OKLAHOMA
k
5
4
3 ARIZONA
0.707914 KANSAS
5
4 ARKANSAS 0.4831379 NORTH DAKOTA
6
5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
9
8 DELAWARE 0.5783029 MISSOURI
525
10
15
INDIANA
MARYLAND
COLORADO
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined.
1.What percent of the refunds are more than $3,500?
2. What percent of the refunds are more than $3500 but less than $3579?
3. What percent of the refunds are more than $3325 but less than $3579?
A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts?
1. Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 44, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the answer of the second part.)
2. Compute the probability of a value greater than 55.0.
Use the same formula, x=55 and subtract the answer from 1.
3. Compute the probability of a value between 52.0 and 55.0.
(The question requires finding probability value between 52 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 52, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the…
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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