Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q4 (page 289)

Distribution of ProportionsEach week, Nielsen Media Research conducts a survey of 5000 households and records the proportion of households tuned to 60Minutes. If we obtain a large collection of those proportions and construct a histogram of them, what is the approximate shape of the histogram?

Short Answer

Expert verified

The histogram will be bell-shaped.

Step by step solution

01

Given information

A survey consisting of 5000 households is conducted. The proportion of households that watch “60 Minutes” is recorded.

02

Sampling distribution of sample proportions

Using the central limit theorem, it is known that the distribution of the sample proportions is normally distributed. Since the distribution of sample proportions is normally distributed, the histogram of such proportions would be bell-shaped.

Here, the sample proportion of households that watch “60 Minutes: is recorded.

A large collection of such sample proportions is considered.

Thus, the distribution of the sample proportion of households that watch “60 Minutes” will be normal. The histogram of such proportions will be bell-shaped.

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

SAT and ACT Tests Because they enable efficient procedures for evaluating answers, multiple choice questions are commonly used on standardized tests, such as the SAT or ACT.

Such questions typically have five choices, one of which is correct. Assume that you must make random guesses for two such questions. Assume that both questions have correct answers of “a.”

a. After listing the 25 different possible samples, find the proportion of correct answers in each sample, then construct a table that describes the sampling distribution of the sample proportions of correct responses.

b. Find the mean of the sampling distribution of the sample proportion.

c. Is the mean of the sampling distribution [from part (b)] equal to the population proportion of correct responses? Does the mean of the sampling distribution of proportions always equal the population proportion?

In Exercises 11–14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in Coca-Cola Zero, Diet Pepsi, Dr Pepper, and Mellow Yello Zero.

Assume that  random samples of size n = 2 are selected with replacement.

Sampling Distribution of the Variance Repeat Exercise 11 using variances instead of means.

In Exercises 13–20, use the data in the table below for sitting adult malesand females (based on anthropometric survey data from Gordon, Churchill, et al.). Thesedata are used often in the design of different seats, including aircraft seats, train seats,theater seats, and classroom seats. (Hint: Draw a graph in each case.)

Sitting Back-to-Knee Length (Inches)

Mean

St. Dev

Distribution

Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

Significance Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) 0.025 and a value is significantly low if P(x or less) 0.025. Find the female back-to-knee length, separating significant values from those that are not significant. Using these criteria, is a female back-to-knee length of 20 in. significantly low?

Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.

z0.15

What is the difference between a standard normal distribution and a non-standard normal distribution?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

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