Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

Videos

Textbook Question

Chapter 8.8, Problem 89E

Refer to Exercise 8.88. Another common insecticide, diazinon, yielded LC50 measurements in three experiments of 7.8, 1.6, and 1.3.

a Estimate the mean LC50 for diazinon, with a 90% confidence interval.
b Estimate the difference between the mean LC50 for DDT and that for diazinon, with a 90% confidence interval. What assumptions are necessary for the method that you used to be valid?

8.88 The Environmental Protection Agency (EPA) has collected data on LC50 measurements (concentrations that kill 50% of test animals) for certain chemicals likely to be found in freshwater rivers and lakes. (See Exercise 7.13 for additional details.) For certain species of fish, the LC50 measurements (in parts per million) for DDT in 12 experiments were as follows:

16 , 5 , 21 , 19 , 1 0 , 5 , 8 , 2 , 7 , 2 , 4 , 9

Estimate the true mean LC50 for DDT with confidence coefficient .90. Assume that the LC50 measurements have an approximately normal distribution.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.8, Problem 88E

Chapter 8.8, Problem 90E

Students have asked these similar questions

Q25. Using the Pearson correlation coefficient, a study on addiction found a positive correlation between time of cravings and time of relapse (r = .51) in a sample of 20 people with a drug addiction. Using a two-tailed test at a .05 level of significance, test whether the correlation is significantly different than 0. Follow the prompts. Step 1. State the hypotheses. A B C D Step 2. Find the critical values. df = _______ CV = +/- (do not include +/-) DO NOT USE eTEXT TABLE C.5 - CVs ARE WRONG. Use table attached to homework instead. _________ Step 4. Make a decision about the null hypothesis. a. Reject H0 b. Retain H0

10.2.23 Find the regression equation, letting overhead width be the predictor (x) variable. Find the best predicted weight of a seal if the overhead width measured from a photograph is 1.9 cm. Can the prediction be correct? What is wrong with predicting the weight in this case? Use a significance level of 0.05. Overhead Width (cm) Weight (kg) 9.4 8.3 7.5 - X 8.2 7.3 9.7 i Critical Values of the Pearson Correlation Coefficient r 195 184 287 246 220 190 Click the icon to view the critical values of the Pearson correlation coefficient r Critical Values of the Pearson Correlation Coefficient r k-0.05 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576 0.553 0.532 0.514 0 497 0.482 0.468 0.456 10.444 The regression equation is y =+x. (Round to one decimal place as needed.) a-0.01 NOTE: To test H: p=0 against H,: p+0, reject H, if the absolute value of in 0.990 0.959 0.917 0.875 0.834 0.798 0.765 0.735 0.708 0.684 0.661 0.641 0.623 0.606 0.590 0.575 0.561 4 16 r is greater than the…

Standard Error is a measure of how much the point estimate changes from sample to sample. The proportion of heads from flipping five coins has a relatively large standard error (SE = .2236), and it is not uncommon to see point estimates from 0% to 100%. The proportion of heads from flipping 1000 coins has a relatively small standard error (SE = .0158), and points estimates will rarely fall outside 45% to 55% heads. Р(1 — р) For proportions, the formula is SE = where n is the sample size and p = p, the sample n proportion (point estimate). Compute the standard error, given a) point estimate = 0.61, null value = 0.7, and n = 120. The standard error = b) point estimate = 0.42, null value = 0.5, and n = 50. The standard error =

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...

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Solution Summary: The author calculates the 90% confidence interval for true mean LC50 for diazinon. The sample mean and standard deviation are calculated as follows.

Concept explainers

Videos

Want to see the full answer?

Chapter 8 Solutions