Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q104SE (page 506)

Is steak your favorite barbeque food? July is National Grilling Month in the United States. On July 1, 2008, The Harris Poll #70 reported on a survey of Americans’ grilling preferences. When asked about their favorite food prepared on a barbeque, 662 of 1,250 randomly sampled Democrats preferred steak, as compared to 586 of 930 randomly sampled Republicans.

a. Give a point estimate for the proportion of all Democrats who prefer steak as their favorite barbeque food.

Short Answer

Expert verified
  1. The point estimate for the proportion of all democrats is 0.5296.

Step by step solution

01

Given Information

The sample size of democrats is 1250.

The sample size of republicans is 930.

And \({x_1} = 662\;and\;{x_2} = 586\)

02

Point Estimate

The value of a sample statistic that is used to estimate the population parameter is called a point estimate. It is a single number. The selected statistic is called a point estimator.

03

Compute Point Estimate

The point estimate for the proportion of all democrats is computed as

\(\begin{aligned}{c}{{\hat p}_1} &= \frac{{{x_1}}}{{{n_1}}}\\ &= \frac{{662}}{{1250}}\\ = 0.5296\end{aligned}\)

Therefore, the point estimate for the proportion of all democrats is 0.5296.

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

Optimal goal target in soccer. When attempting to score a goal in soccer, where should you aim your shot? Should you aim for a goalpost (as some soccer coaches teach), the middle of the goal, or some other target? To answer these questions, Chance (Fall 2009) utilized the normal probability distribution. Suppose the accuracy x of a professional soccer player’s shots follows a normal distribution with a mean of 0 feet and a standard deviation of 3 feet. (For example, if the player hits his target,x=0; if he misses his target 2 feet to the right, x=2; and if he misses 1 foot to the left,x=-1.) Now, a regulation soccer goal is 24 feet wide. Assume that a goalkeeper will stop (save) all shots within 9 feet of where he is standing; all other shots on goal will score. Consider a goalkeeper who stands in the middle of the goal.

a. If the player aims for the right goalpost, what is the probability that he will score?

b. If the player aims for the center of the goal, what is the probability that he will score?

c. If the player aims for halfway between the right goal post and the outer limit of the goalkeeper’s reach, what is the probability that he will score?

The data for a random sample of six paired observations are shown in the next table.

a. Calculate the difference between each pair of observations by subtracting observation two from observation 1. Use the differences to calculate d¯andsd2.

b. If μ1andμ2are the means of populations 1 and 2, respectively, expressed μdin terms of μ1andμ2.

PairSample from Population 1

(Observation 1)

Sample from Population 2(Observation 2)
123456739648417247

c. Form a 95% confidence interval for μd.

d. Test the null hypothesis H0:μd=0against the alternative hypothesis Ha:μd≠0. Useα=.05 .

Question: Forecasting daily admission of a water park. To determine whether extra personnel are needed for the day, the owners of a water adventure park would like to find a model that would allow them to predict the day’s attendance each morning before opening based on the day of the week and weather conditions. The model is of the form

where,

y = Daily admission

x1 = 1 if weekend

0 otherwise

X2 = 1 if sunny

0 if overcast

X3 = predicted daily high temperature (°F)

These data were recorded for a random sample of 30 days, and a regression model was fitted to the data.

The least squares analysis produced the following results:

with

  1. Interpret the estimated model coefficients.
  2. Is there sufficient evidence to conclude that this model is useful for predicting daily attendance? Use α = .05.
  3. Is there sufficient evidence to conclude that the mean attendance increases on weekends? Use α = .10.
  4. Use the model to predict the attendance on a sunny weekday with a predicted high temperature of 95°F.
  5. Suppose the 90% prediction interval for part d is (645, 1,245). Interpret this interval.

Business sign conservation. The Federal Highway Administration (FHWA) lately issued new guidelines for maintaining and replacing business signs. Civil masterminds at North Carolina State University studied the effectiveness of colorful sign conservation practices developed to cleave to the new guidelines and published the results in the Journal of Transportation Engineering (June 2013). One portion of the study concentrated on the proportion of business signs that fail the minimal FHWA retro-reflectivity conditions. Of signs maintained by the. North Carolina Department of Transportation (NCDOT), .512 were supposed failures. Of signs maintained by. County- possessed roads in North Carolina, 328 were supposed. Failures. Conduct a test of the thesis to determine whether the true proportions of business signs that fail the minimal FHWA retro-reflectivity conditions differ depending on whether the signs are maintained by the NCDOT or by the county. Test using α = .05

Question: The speed with which consumers decide to purchase a product was investigated in the Journal of Consumer Research (August 2011). The researchers theorized that consumers with last names that begin with letters later in the alphabet will tend to acquire items faster than those whose last names begin with letters earlier in the alphabet—called the last name effect. MBA students were offered free tickets to an event for which there was a limitedsupply of tickets. The first letter of the last name of those who responded to an email offer in time to receive the tickets was noted as well as the response time (measured in minutes). The researchers compared the response times for two groups of MBA students: (1) those with last names beginning with one of the first nine letters of the alphabet and (2) those with last names beginning with one of the last nine letters of the alphabet. Summary statistics for the two groups are provided in the table.

First 9

Letters: A–I

Last 9

Letters: R–Z

Sample size

25

25

Mean response time (minutes)

25.08

19.38

Standard deviation (minutes)

10.41

7.12

Source: Based on K. A. Carlson and J. M. Conrad, “The Last Name Effect: How Last Name Influences Acquisition Timing,” Journal of Consumer Research, Vol. 38, No. 2, August 2011.

a. Construct a 95% confidence interval for the difference between the true mean response times for MBA students in the two groups.

b. Based on the interval, part a, which group has the shorter mean response time? Does this result support the researchers’ last name effect theory? Explain.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Probability and 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