/*! 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} Q. 37 Do you drink cereal milk? What s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q. 37 (page 440)

Do you drink cereal milk? What sample size would be required to reduce the standard deviation of the sampling distribution to one-half the value you found in Exercise 35(b)? Justify your answer.

Short Answer

Expert verified

Sample size would be required to reduce the standard deviation of the sampling distribution to one-half the value you found in Exercise 35(b) is4048.

Step by step solution

01

Concept Introduction

The sampling distribution's mean difference indicates how much the sample statistic changes from sample to sample.

By a factor of n, it is smaller than the population standard deviation.

Individual observations are more variable than averages.

02

Explanation 

Given:

n=1012

The standard deviation formula is:

蟽p^=p(1-p)n

In order to reduce the standard deviation to half of its existing value, then:

localid="1650086574157" 蟽p^2=12脳p(1鈭�p)n=p(1鈭�p)4n

Let quadrupling the sample size:

localid="1650086582641" 4n=4(1012)n=4048

Hence, the required sample size is 4048.

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

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5,but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation0.7.

(a) What are the mean and standard deviation of the average number of moths xin50traps?

(b) Use the central limit theorem to help you find the probability that the average number of moths in 50traps is greater than0.6.

Stop the carl A car company has found that the lifetime of its disc brake pads varies from car to car according to a Normal distrilustion with mean 渭=55000miles and standard deviation蟽=4500miles. The company installs a new brand of brake pads on an SRS of 8cars.

(a) If the new brand has the same lifetime distribution as the previous bye of brake pad, what is the sampling distribution of the mean lifetime x?

(b) The average life of the pads an these 8cars turns out to be x=51800miles. Find the probability that the sample mean lifetime is 51800miles or less if the lifetime distribution is unchanged, What conclusion would you draw?

The candy machine Suppose a large candy machine has 15% orange candies. Use Figure 7.13 (page 435) to help answer the following questions.

(a) Would you be surprised if a sample of 25 candies from the machine contained 8 orange candies (that's 32%orange)? How about 5 orange candies (orange)? Explain.

(b) Which is more surprising: getting a sample of 25 candies in which localid="1649737645698" 32%are orange or getting a sample of 50 candies in which localid="1649737650189" 32%are orange? Explain.

The candy machine Suppose a large candy machine has 15%orange candies. Use Figure 7.13 (page 435) to help answer the following questions.

(a) Would you be surprised if a sample of 25 candies from the machine contained 8 orange candies (that's 32%orange)? How about 5 orange candies ( 20%orange)? Explain.

(b) Which is more surprising: getting a sample of 25 candies in which 32%are orange or getting a sample of 50 candies in which 32% are orange? Explain.

Bottling cola A hattling compamy uses a fillimg maichine to fill plastic botles with cola. The bottles are supposed to contain 300milliliters (ml) . In fact, the contents vary according to a Normal distribution with mean 渭=298ml and standard deviation 蟽=3ml

(a) What is the probability that in individual bottle contains less than 295ml? Show you work.

(b) What is the probability that the mean contents of six randomly selected bottles is less than 295ml? Show your work.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.