/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q77E USGA golf ball tests. The United... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q77E (page 364)

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?

Short Answer

Expert verified

Iron Byron needs hit 271 golf balls to reach the desired reliability in determining the mean.

Step by step solution

01

Given information

The USGA wants to estimate the average distance for a new brand to within one yard with 90 percent certainty. Suppose that previous tests have revealed that the normal variation of Iron Byron's golf ball distances is roughly 10 yards

02

Finding the sample size

The standard error is 1 in this case.

The standard deviation value is 10.

A 90% confidence interval's critical value isz伪/2=z0.10/2=z0.05=1.645

So, the standard error is,

SE=z伪/2蟽nn=z2伪/2蟽2SE2n=1.6452脳10212n=270.6025n鈮�271

Iron Byron needs hit 271 golf balls to reach the necessary accuracy in determining the mean.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Question: The mean and standard deviation of a random sample of n measurements are equal to 33.9 and 3.3, respectively.

a. Find a 95% confidence interval for 渭if n = 100.

b. Find a 95% confidence interval for渭 if n = 400.

c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

Corporate sustainability of CPA firms. Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 6.12 (p. 339). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992 senior managers at CPA firms. The accompanying Minitab printout gives 90% confidence intervals for both the variance and standard deviation of level of support for all senior managers at CPA firms.

a. Locate the 90% confidence interval for 蟽2on the printout. Interpret the result. b. Use the sample variance on the printout to calculate the 90% confidence interval for蟽2. Does your result agree with the interval shown on the printout?

c. Locate the 90% confidence interval for on the printout.

d. Use the result, part a, to calculate the 90% confidence interval for蟽. Does your result agree with the interval shown on the printout?

e. Give a practical interpretation of the 90% confidence interval for.蟽

f. What assumption about the distribution of level of support is required for the inference, part e, to be valid? Is this assumption reasonably satisfied? (Use your answer to Exercise 4.125, p. 270.)

Oil content of fried sweet potato chips. The characteristics of sweet potato chips fried at different temperatures were investigated in the Journal of Food Engineering (September 2013). A sample of 6 sweet potato slices was fried at 130掳 using a vacuum fryer. One characteristic of interest to the researchers was internal oil content (measured in millions of grams). The results were: x炉=178and s=11. The researchers are interested in estimating the variance of the interval oil content measurements for sweet potato chips.

a. Identify the target parameter, in symbols and words.

b. Compute a 95% confidence interval for 蟽2.

c. What does it mean to say that the target parameter lies within the interval with 鈥�95% confidence鈥�?

d. What assumption about the data must be satisfied in order for the confidence interval to be valid?

e. To obtain a practical interpretation of the interval, part b, explain why a confidence interval for the standard deviation, 蟽, is desired.

f. Use the results, part b, to compute a 95% confidence interval for蟽 . Give a practical interpretation of the interval.

Largest private companies. IPOs鈥攊nitial public offerings of stock鈥攃reate billions of dollars of new wealth for owners, managers, and employees of companies that were previously privately owned. Nevertheless, hundreds of large and thousands of small companies remain privately owned. The revenues of a random sample of 15 firms from Forbes 216 Largest Private Companies list are given in the table below

a. Describe the population from which the random sample was drawn.

b. Use a 98% confidence interval to estimate the mean revenue of the population of companies in question

c. Interpret your confidence interval in the context of the problem

d. What characteristic must the population possess to ensure the appropriateness of the estimation procedure used in part b?

e. Suppose Forbes reports that the true mean revenue of the 216 companies on the list is $5.0 billion. Is the claim believable?

Question: Heart rate variability of police officers. Are police officers susceptible to higher-than-normal heart rates? The heart rate variability (HRV) of police officers was the subject of research published in the American Journal of Human Biology (January 2014). HRV is defined as the variation in time intervals between heartbeats. A measure of HRV was obtained for each in a sample of 355 Buffalo, N.Y., police officers. (The lower the measure of HRV, the more susceptible the officer is to cardiovascular disease.) For the 73 officers diagnosed with hypertension, a 95% confidence interval for the mean HRV was (4.1, 124.5). For the 282 officers who are not hypertensive, a 95% confidence interval for the mean HRV was (148.0, 192.6).

a. What confidence coefficient was used to generate the confidence intervals?

b. Give a practical interpretation of both 95% confidence intervals. Use the phrase 鈥�95% confident鈥� in your answer.

c. When you say you are 鈥�95% confident,鈥� what do you mean?

d. If you want to reduce the width of each confidence interval, should you use a smaller or larger confidence coefficient? Explain.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.