Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q117SE (page 376)

Water pollution testing. The EPA wants to test a randomlyselected sample of n water specimens and estimate themean daily rate of pollution produced by a mining operation.If the EPA wants a 95% confidence interval estimatewith a sampling error of 1 milligram per liter (mg/L),how many water specimens are required in the sample?Assume prior knowledge indicates that pollution readingsin water samples taken during a day are approximately

normally distributed with a standard deviation equal to5 mg/L.

Short Answer

Expert verified

The number of water specimens required in the sample are n=97.

Step by step solution

01

Given Information

In water pollution testing the EPA is randomly selecting a sample with n water specimens to estimate the mean daily rate of pollution. The EPA wants a confidence interval of 95% level of significance with a sampling error of 1 mg/L.

The prior knowledge tells that the sample standard deviation is 5mg/L.

02

Step 2:Defining the parameters

Therefore, the parameters here are:

σ=5mg/LS.E.=1mg/LCI=0.95

Now, the formula for sampling error is:

S.E.=z×σn

Also, the z value for 0.95 confidence interval is 1.96

Step 2:Substituting the values

S.E.=z×σn1=1.96×5nn=9.8n=96.04n≈97

Therefore, n=97 water specimens are required

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

USGA golf ball tests. The United States Golf Association (USGA) tests all new brands of golf balls to ensure that they meet USGA specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine called "Iron Byron," a name inspired by the swing of the famous golfer Byron Nelson. Suppose the USGA wishes to estimate the mean distance for a new brand to within 1 yard with 90% confidence. Assume that

past tests have indicated that the standard deviation of the distances Iron Byron hits golf balls is approximately 10 yards. How many golf balls should be hit by Iron Byron to achieve the desired accuracy in estimating the mean?

Customers who participate in a store’s free loyalty card program save money on their purchases but allow the store to keep track of their shopping habits and potentially sell these data to third parties. A Pew Internet & American Life Project Survey (January 2016) revealed that half (225) of a random sample of 250 U.S. adults would agree to participate in a store loyalty card program, despite the potential for information sharing.

a. Estimate the true proportion of all U.S. adults who would agree to participate in a store loyalty card program, despite the potential for information sharing.

b. Form a 90% confidence interval around the estimate, part a.

c. Provide a practical interpretation of the confidence interval, part b. Your answer should begin with, “We are 90% confident . . .”

d. Explain the theoretical meaning of the phrase, “We are 90% confident.”

Wear-out of used display panels. Refer to Exercise 4.126 (p. 270) and the study of the wear-out failure time of used colored display panels purchased by an outlet store. Recall that prior to acquisition, the panels had been used for about one-third of their expected lifetimes. The failure times (in years) for a sample of 50 used panels are reproduced in the table. An SPSS printout of the analysis is shown below.

a. Locate a 95% confidence interval for the true mean failure time of used colored display panels on the printout.

b. Give a practical interpretation of the interval, part a.

c. In the repeated sampling of the population of used colored display panels, where a 95% confidence interval for the mean failure time is computed for each sample, what proportion of all the confidence intervals generated will capture the true mean failure time?

Describe the sampling distribution of based on large samples of size n—that is, give the mean, the standard deviation, and the (approximate) shape of the distribution of when large samples of size n are (repeatedly) selected fromthe binomial distribution with probability of success p.

Unethical corporate conduct. How complicit are entrylevel accountants in carrying out an unethical request from their superiors? This was the question of interest in a study published in the journal Behavioral Research in Accounting (July 2015). A sample of 86 accounting graduate students participated in the study. After asking the subjects to perform what is clearly an unethical task (e.g., to bribe a customer), the researchers measured each subject’s intention to comply with the unethical request score. Scores ranged from -1.5 (intention to resist the unethical request) to 2.5 (intention to comply with the unethical request). Summary statistics on the 86 scores follow: x¯=2.42,s=2.84.

a. Estimate μ, the mean intention to comply score for the population of all entry-level accountants, using a 90% confidence interval.

b. Give a practical interpretation of the interval, part a.

c. Refer to part a. What proportion of all similarly constructed confidence intervals (in repeated sampling) will contain the true value of μ?

d. Compute the interval, x¯±2s. How does the interpretation of this interval differ from that of the confidence interval, part a?

See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free