A streaming service company plans to introduce a new premium tier and wants to estimate the worldwide percentage of its users who intend to subscribe. Based on a pilot, 20%20\% of users indicated they plan to upgrade. The marketing team needs a 90%90\% confidence interval with a margin of error of 33 percentage points. How many users must be surveyed? Can the team simply poll their own friends and colleagues instead of drawing a random sample? Explain.

Table of contents

Prepare for your exams

Upload your syllabus and get recommendations on what to study and when. No syllabus? Sharing your exam schedule works too.

Skip topic navigation

1. Intro to Stats and Collecting Data(0)

Intro to Stats
(0)

Levels of Measurement
(0)

Intro to Collecting Data
(0)

Sampling Methods
(0)

2. Describing Data with Tables and Graphs(0)

Visualizing Qualitative vs. Quantitative Data
(0)

Frequency Distributions
(0)

Histograms
(0)

Bar Graphs and Pareto Charts
(0)

Pie Charts
(0)

Frequency Polygons
(0)

Dot Plots
(0)

Stemplots (Stem-and-Leaf Plots)
(0)

Time-Series Graph
(0)

3. Describing Data Numerically(0)

Mean
(0)

Median
(0)

Mode
(0)

Standard Deviation
(0)

Interpreting Standard Deviation
(0)

Percentiles & Quartiles
(0)

Boxplots
(0)

4. Probability(0)

Basic Concepts of Probability
(0)

Complements
(0)

Addition Rule
(0)

Multiplication Rule: Independent Events
(0)

Introduction to Contingency Tables
(0)

Multiplication Rule: Dependent Events
(0)

Bayes' Theorem
(0)

Fundamental Counting Principle
(0)

Counting
(0)

5. Binomial Distribution & Discrete Random Variables(0)

Discrete Random Variables
(0)

Binomial Distribution
(0)

Poisson Distribution
(0)

Hypergeometric Distribution
(0)

6. Normal Distribution and Continuous Random Variables(0)

Uniform Distribution
(0)

Standard Normal Distribution
(0)

Non-Standard Normal Distribution
(0)

7. Sampling Distributions & Confidence Intervals: Mean(0)

Sampling Distribution of the Sample Mean and Central Limit Theorem
(0)

Introduction to Confidence Intervals
(0)

Confidence Intervals for Population Mean
(0)

Determining the Minimum Sample Size Required
(0)

8. Sampling Distributions & Confidence Intervals: Proportion(0)

Sampling Distribution of Sample Proportion
(0)

Confidence Intervals for Population Proportion
(0)

Chi Square Distribution
(0)

Confidence Intervals for Population Variance
(0)

9. Hypothesis Testing for One Sample(0)

Steps in Hypothesis Testing
(0)

Performing Hypothesis Tests: Means
(0)

Performing Hypothesis Tests: Proportions
(0)

Performing Hypothesis Tests: Variance
(0)

Critical Values and Rejection Regions
(0)

Link Between Confidence Intervals and Hypothesis Testing
(0)

Type I & Type II Errors
(0)

10. Hypothesis Testing for Two Samples(0)

Two Proportions
(0)

Two Means - Unknown, Unequal Variance
(0)

Two Means - Unknown, Equal Variance
(0)

Two Means - Known Variance
(0)

Two Means - Matched Pairs (Dependent Samples)
(0)

Two Variances and F Distribution
(0)

11. Correlation(0)

Scatterplots & Intro to Correlation
(0)

Correlation Coefficient
(0)

12. Regression(0)

Linear Regression & Least Squares Method
(0)

Residuals
(0)

Coefficient of Determination
(0)

Inferences for Slope
(0)

Prediction Intervals
(0)

Quadratic Regression
(0)

13. Chi-Square Tests & Goodness of Fit(0)

Goodness of Fit Test
(0)

Contingency Tables
(0)

Independence Tests
(0)

Homogeneity Tests
(0)

14. ANOVA(0)

Introduction to ANOVA
(0)

Multiple Comparisons: Tukey Test
(0)

Multiple Comparisons: Tukey-Kramer Test
(0)

Multiple Comparisons: Bonferoni Test
(0)

Two-Way ANOVA
(0)

8. Sampling Distributions & Confidence Intervals: Proportion

Confidence Intervals for Population Proportion

8. Sampling Distributions & Confidence Intervals: Proportion

Confidence Intervals for Population Proportion: Videos & Practice Problems

Video Lessons Practice Worksheet

Back to all problems

39 of 0

PreviousNext

Problem 39Multiple Choice

A streaming service company plans to introduce a new premium tier and wants to estimate the worldwide percentage of its users who intend to subscribe. Based on a pilot, $20 percent sign$ of users indicated they plan to upgrade. The marketing team needs a $90 percent sign$ confidence interval with a margin of error of $3$ percentage points. How many users must be surveyed? Can the team simply poll their own friends and colleagues instead of drawing a random sample? Explain.

$658$

Yes, because with $n equals 482$ , the central limit theorem applies, and any sample (even friends) will give an approximately valid margin of error.

$482$

No. Polling friends is a convenience sample that introduces selection bias and breaks the random sampling assumption, so the $90 percent sign$ CI would not be valid.

$598$

Yes, if they can post‐stratify (weight) the friends’ responses to match known user demographics, correcting for the bias.

$344$

No. Unless they can show that their friends’ upgrade intentions are exchangeable with the global population, the sample will be a valid generalization.

0 Comments

Download the Mobile app

Accessibility

Privacy

Do not sell my personal information