Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q. 39 (page 441)

A sample survey interviews an SRS of 267college women. Suppose (as is roughly true) that 70%of college women have been on a diet within the past12months. What is the probability that 75%or more of the women in the sample have been on a diet? Follow the four-step process.

Short Answer

Expert verified

The probability that 75%or more of the women in the sample have been on a dietP(p^≥75%)=0.0375.

Step by step solution

01

Given Information

Given

p=70%=0.70

p^=75%=0.75

n=267

02

Explanation

The mean of the sampling distribution of p^is equal to the population proportion p:

μp^=p=0.70

The standard deviation of the sampling distribution of p^is:

σp^=p(1-p)n=0.70(1-0.70)267≈0.0280449

The z-score is the value decreased by the mean, divided by the standard deviation:

z=x-μσ=0.75-0.700.0280449≈1.78

Determine the corresponding probability using table A:

P(p^≥75%)=P(z>1.78)=P(Z<-1.78)=0.0375

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

The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. At both schools, a simple random sample of about 3%of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p=0.80at both schools. Which of the following is the best conclusion?

(a) The estimate from Johns Hopkins has less sampling variability than that from Ohio State.

(b) The estimate from Johns Hopkins has more sampling variability than that from Ohio State.

(c) The two estimates have about the same amount of sampling variability.

(d) It is impossible to make any statement about the sampling variability of the two estimates since the students surveyed were different.

(e) None of the above

3. Describe the shape of the

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all 222recorded eruptions during a particular month. For this population, the median is 75minutes. We used Fathom software to take500SRSs of size 10from the population. The 500values of the sample median are displayed in the histogram above right. The mean of the 500sample median values is 73.5.

Sampling distribution. Explain what this means in terms of overestimating or underestimating the population median

Mars, Incorporated, says that the mix of colors in its M&M’S® Milk Chocolate Candies is 24%blue, 20%orange, 16%green,14%yellow, 13%red, and 13%brown. Assume that the company’s claim is true. We want to examine the proportion of orange M&M’S in repeated random samples of 50candies. Which of the graphs that follow could be the approximate sampling distribution of the statistic? Explain your choice

Predict the election Just before a presidential election, a national opinion poll increases the size of its weekly random sample from the usual 1500 people to 4000 people.

(a) Does the larger random sample reduce the bias of the poll result? Explain.

(b) Does it reduce the variability of the result? Explain

Squirrels and their food supply (3.2) Animal species produce more offspring when their supply of food goes up. Some animals appear able to anticipate unusual food abundance. Red squirrels eat seeds from pinecones, a food source that sometimes has very large crops. Researchers collected data on an index of the abundance of pinecones and the average number of offspring per female over 16years. Computer output from a least-squares regression on these data and a residual plot.

(a) Give the equation for the least-squares regression line. Define any variables you use.

(b) Explain what the residual plot tells you about how well the linear model fits the data.

(c) Interpret the values of r2and s in context.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

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