Math Problem Statement

A survey of the US population found that 26% of consumers shop for groceries online.  Suppose you select a sample of 200 consumers. Using what you know about the distribution of the sample proportion answer the following question.

Suppose instead you take a sample of 800 consumers. What is the probability that between 23% and 29% of consumers in your sample shop for groceries online?

(Round answers to four decimal places.)

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Sampling Distribution
Normal Distribution
Probability

Formulas

Sample Proportion: p̂ = x / n
Standard Error: SE = sqrt[p(1-p)/n]
Z-score: Z = (p̂ - p) / SE
Probability Calculation using Normal Distribution

Theorems

Central Limit Theorem

Suitable Grade Level

Undergraduate Statistics