Please provide the following information for Problems 11-22. part (a): (i) What is the level of significance? State the null and alternate hypotheses. (ii)Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (iii)Find (or estimate) the P -value. Sketch the sampling distribution and show the area corresponding to the P -value. (iv)Based on your answers in parts (i)—(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? (v) Interpret your conclusion in the context of the application. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P -value a small amount, and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding. Environment: Pollution Index Based on information from the Denver Post , a random sample of n 1 = 12 winter days in Denver gave a sample mean pollution index of x ¯ 1 = 43 . Previous studies show that σ 1 = 21 . For Englewood (a suburb of Denver), a random sample of n 2 = 14 winter days gave a sample mean pollution index of x ¯ 2 = 36 . Previous studies show that σ 2 = 21 . Assume the pollution index is normally distributed in both Englewood and Denver. (a) Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (b) Find a 99% confidence interval for µ 1 − µ 2 . Explain the meaning of the confidence interval in the context of the problem.

BuyFind

Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075
BuyFind

Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075

Solutions

Chapter
Section
Chapter 10.2, Problem 12P
Textbook Problem

Please provide the following information for Problems 11-22. part (a):

(i) What is the level of significance? State the null and alternate hypotheses.

(ii)Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.

(iii)Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(iv)Based on your answers in parts (i)—(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?

(v)Interpret your conclusion in the context of the application.

Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount, and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding.

Environment: Pollution Index Based on information from the Denver Post, a random sample of n 1 =   12 winter days in Denver gave a sample mean pollution index of x ¯ 1 =   43 . Previous studies show that σ 1   =   21 . For Englewood (a suburb of Denver), a random sample of n 2 = 14 winter days gave a sample mean pollution index of x ¯ 2 =   36 . Previous studies show that σ 2   =   21 . Assume the pollution index is normally distributed in both Englewood and Denver.

(a) Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance.

(b) Find a 99% confidence interval for µ 1   µ 2 . Explain the meaning of the confidence interval in the context of the problem.

Expert Solution

Want to see the full answer?

Check out a sample textbook solution.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.

Chapter 10 Solutions

Understanding Basic Statistics
Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - For Problems 9-17 assume that the distribution of...Ch. 10.1 - Expand Your Knowledge: Confidence Intervals for d...Ch. 10.1 - Critical Region Method: Student's t Solve Problem...Ch. 10.1 - Critical Region Method: Students t Solve Problem...Ch. 10.2 - Statistical Literacy Consider a hypothesis test of...Ch. 10.2 - Statistical Literacy Consider a hypothesis test of...Ch. 10.2 - Statistical Literacy Consider a hypothesis test of...Ch. 10.2 - Critical Thinking When conducting a lest of the...Ch. 10.2 - Critical Thinking Josh and Kendra each calculated...Ch. 10.2 - Critical Thinking If a 90% confidence interval for...Ch. 10.2 - Basic Computation: Paired Differences Test For a...Ch. 10.2 - Basic Computation: Texting 12 Two populations have...Ch. 10.2 - Basic Computation: Testing- 12 A random sample of...Ch. 10.2 - Basic Computation: Testing 12 Two populations have...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Please provide the following information for...Ch. 10.2 - Expand Your Knowledge: Software Approximation for...Ch. 10.2 - Expand Your Knowledge: Pooled Two-Sample Procedure...Ch. 10.2 - Critical Region Method: Testing 12;1,2 Unknown...Ch. 10.2 - Critical Region Method: Testing 12;1,2Known Redo...Ch. 10.3 - Statistical Literacy Consider a hypothesis test of...Ch. 10.3 - Statistical Literacy Consider a hypothesis test of...Ch. 10.3 - Critical Thinking Consider two independent...Ch. 10.3 - Critical Thinking If a 90% confidence interval for...Ch. 10.3 - Basic Computation: Testing p1p2 For one binomial...Ch. 10.3 - Basic Computation: Testing p1p2 For one binomial...Ch. 10.3 - Federal Tax Money: Art Funding Would you favor...Ch. 10.3 - Art Funding: Politics Would you favor spending...Ch. 10.3 - Sociology: Trusting People Generally speaking,...Ch. 10.3 - Political Science: Voters This problem is based on...Ch. 10.3 - Extraterrestrials: Believe It? Based on...Ch. 10.3 - Art: Polities Do you prefer paintings in which the...Ch. 10.3 - Critical region Method: Testing p1p2 Redo Problem...Ch. 10.3 - Critical Region Method: Testing p1p2 Redo Problem...Ch. 10.3 - Basic Computation: Confidence Inters al for p1p2...Ch. 10.3 - Basic Computation: Confidence Interval for p1p2...Ch. 10.3 - Myers-Briggs: Marriage Counseling Isabel Myers was...Ch. 10.3 - Myers-Briggs: Marriage Counseling Most married...Ch. 10.3 - Navajo Culture: Traditional Hogans S. C. Jett is a...Ch. 10.3 - Archaeology: Cultural Affiliation "Unknown...Ch. 10.3 - Critical Thinking: Different Confidence Levels (a)...Ch. 10.3 - Focus Problem: Wood Duck Nests In the Focus...Ch. 10 - Statistical Literacy and Terminology When are two...Ch. 10 - 2. Statistical Literacy and Terminology When are...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - For each hypothesis test in Problems 3-10, please...Ch. 10 - Sweets May Not Be Culprit in Hyper Kids was a USA...Ch. 10 - In there a relationship between confidence...

Additional Math Textbook Solutions

Find more solutions based on key concepts
For the following scores, find the value of each expression: X 3 2 4 2 a. X b. (X)2 c. X 2 d. (X 2)

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Find a b. 2. a = 5, 2, b = 3, 4

Multivariable Calculus

In Exercises 13-20, sketch a set of coordinate axes and plot each point. 18. (52,32)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In Problems 33 – 38, solve each inequality. 38.

Mathematical Applications for the Management, Life, and Social Sciences

Solve each equation and check: 6(17x)=24x

Elementary Technical Mathematics

Prove the statement using the precise definition of a limit. limx0x3=0

Single Variable Calculus: Early Transcendentals

Which definite integral is the volume of the solid obtained by revolving the region at the right about the y-ax...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Graph each equation. 12(x2y)=y1

College Algebra (MindTap Course List)

Hotel Price Comparison. Suppose that you are responsible for making arrangements for a business convention and ...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Marginal Tax Rate You have the opportunity to earn some extra income working at $20perhour. If your marginal ta...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Spring/Mass Systems: Free Undamped Motion A force of 400 newtons stretches a spring 2 meters. A mass of 50 kilo...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)