/*! 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} Problem 48 According to a 2018 Pew Research... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 48

According to a 2018 Pew Research Center report on social media use, \(28 \%\) of American adults use Instagram. Suppose a sample of 150 American adults is randomly selected. We are interested in finding the probability that the proportion of the sample who use Instagram is greater than \(30 \%\). a. Without doing any calculations, determine whether this probability will be greater than \(50 \%\) or less than \(50 \%\). Explain your reasoning. b. Calculate the probability that the sample proportion is \(30 \%\) or more.

Short Answer

Expert verified
a. The probability that the proportion of the sample who use Instagram is greater than 30% is less than 50% because 30% is greater than the population proportion of 28%. b. The calculated probability for more than 30% using Instagram in the selected sample needs the final value from step 5.

Step by step solution

01

Reasoning

Given the population proportion (p) of American adults who use Instagram is 28%. If we are randomly selecting American adults, it is more likely that the sample proportion will be close to the population proportion rather than far from it. Therefore, the probability that more than 30% of the sampled adults using Instagram would be less than 50% since 30% is greater than the given population proportion of 28%.
02

Set Up The Variables

To solve for part b of the exercise, we need to set up the variables appropriate for this statistics problem. We know that the sample size (n) = 150, the population proportion (p) = 0.28 and we need to find the sample proportion greater than or equal to 0.30.
03

Estimate the Mean and Standard Deviation

First, calculate the mean (渭) and standard deviation (蟽) of the sample distribution. The mean of the distribution of sample proportions equals to the population proportion, 渭 = p = 0.28. The standard deviation of the distribution of sample proportions is calculated as \(\sqrt{ ( p * ( 1 - p ) ) / n }\) = \(\sqrt{ (0.28 * 0.72) / 150 }\).
04

Find the Z-Score

After obtaining the values of 渭 and 蟽, calculate the Z-score for the sample proportion (.30). The formula is Z = (sample proportion - 渭) / 蟽. By substituting the values we will find the Z score is equal to: (0.30 - 0.28) / 蟽.
05

Calculate the Probability

Finally, using the calculated Z score and the standard normal distribution table (Z-table) or a calculator with normal distribution probability capability, the probability can be found that the sample proportion is 30% or more. That is P(Z 鈮� calculated Z value).

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

Maria opposes capital punishment and wants to find out if a majority of voters in her state support it. She goes to a church picnic and asks everyone there for their opinion. Because most of them oppose capital punishment, she concludes that a vote in her state would go against it. Explain what is wrong with Maria's approach.

You are receiving a large shipment of batteries and want to test their lifetimes. Explain why you would want to test a sample of batteries rather than the entire population.

Find the sample size required for a margin of error of 3 percentage points, and then find one for a margin of error of \(1.5\) percentage points; for both, use a \(95 \%\) confidence level. Find the ratio of the larger sample size to the smaller sample size. To reduce the margin of error to half, by what do you need to multiply the sample size?

According to a 2018 Rasmussen Poll, \(40 \%\) of American adults were very likely to watch some of the Winter Olympic coverage on television. The survey polled 1000 American adults and had a margin of error of plus or minus 3 percentage points with a \(95 \%\) level of confidence. a. State the survey results in confidence interval form and interpret the interval. b. If the Rasmussen Poll was to conduct 100 such surveys of 1000 American adults, how many of them would result in confidence intervals that included the true population proportion? c. Suppose a student wrote this interpretation of the confidence interval: "We are \(95 \%\) confident that the sample proportion is between \(37 \%\) and \(43 \%\)." What, if anything, is incorrect in this interpretation?

Explain the difference between sampling with replacement and sampling without replacement. Suppose you have the names of 10 students, each written on a 3 -inch by 5 -inch notecard, and want to select two names. Describe both procedures.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.