Tweet, tweet! What proportion of students at your school use Twitter? To find out, you survey a simple random sample of students from the school roster.

a. Will your sample result be exactly the same as the true population proportion? Explain your answer.

b. Which would be more likely to produce a sample result closer to the true population value: an SRS of 50students or an SRS of 100students? Explain your answer.

Short Answer

Expert verified

a.No, our sample result will not be exactly the same as the true population proportion.

b.An SRS of 100students would be more likely to produce a sample result closer to the true population value than an SRS of 50students.

Step by step solution

01

Part (a) Step 1: Given Information 

We need to find out whether sample result will be same as true population proportion

02

Part (a) Step 2: Explanation

No, our sample result will not be exactly the same as the true population proportion because different random samples will produce different statistics, and it is unlikely that this will match that parameter exactly.

03

Part (b) Step 1: Given Information

We are given two random samples of students.

50students random samples

100students random samples

We need to explain which sample will give result closer to true population value

04

Part (b) Step 2: Explanation

An SRS of 100 students would be more likely to produce a sample result closer to the true population value than an SRS of 50 students because on increasing the sample size, there is a reduction in the variability.

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 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

Unequal benefitsResearchers on aging proposed investigating the effect of

supplemental health services on the quality of life of older people. Eligible patients on

The rolls of a large medical clinic were to be randomly assigned to treatment and control.

groups. The treatment group would be offered hearing aids, dentures, transportation, and other services not available without charge to the control group. The review board believed that providing these services to some but not other people in the same institution raised ethical questions. Do you agree?

Stronger players A football coach hears that a new exercise program will increase upper-body strength better than lifting weights. He is eager to test this new program in the off-season with the players on his high school team. The coach decides to let his players choose which of the two treatments they will undergo for3weeks—exercise or weight lifting. He will use the number of push-ups a player can do at the end of the experiment as the response variable. Which principle of experimental design does the coach’s plan violate? Explain how this violation could lead to confounding.

High-speed Internet Laying fiber-optic cable is expensive. Cable companies want to make sure that if they extend their lines to less dense suburban or rural areas, there will be sufficient demand so the work will be cost-effective. They decide to conduct a survey to determine the proportion of households in a rural subdivision that would buy the service. They select a simple random sample of 5blocks in the subdivision and survey each family that lives on one of those blocks.

a. What is the name for this kind of sampling method?

b. Give a possible reason why the cable company chose this method.

Growing in the shade- The ability to grow in shade may help pine trees found in the dry forests of Arizona to resist drought. How well do these pines grow in shade? Investigators planted pine seedlings in a greenhouse in either full light, light reduced to 25% of normal by shade cloth, or light reduced to 5% of normal. At the end of

the study, they dried the young trees and weighed them. Identify the experimental units and the treatments.

Do you trust the Internet? You want to ask a sample of high school students the question “How much do you trust information about health that you find on the Internet—a great deal, somewhat, not much, or not at all?” You try out this and other questions on a pilot group of 5students chosen from your class.

a. Explain how you would use a line of Table D to choose an SRS of 5students from the following list.

b. Use line 107to select the sample. Show how you use each of the digits.

See all solutions

Recommended explanations on Math Textbooks

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