Math Problem Statement

A market researcher for a provider of music player accessories wants to know the proportion of customers who own cars to assess the market for a new car charger. A survey of 500 customers indicates that 74​% own cars. ​a) What is the estimated standard deviation of the sampling distribution of the​ proportion? ​b) How large would the estimated standard deviation have been if he had surveyed only 125 customers​ (assuming the proportion is about the​ same)? Question content area bottom Part 1 ​a) The estimated standard deviation of the sampling distribution of the proportion is    enter your response here. ​(Round to four decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Proportions
Sampling Distribution
Standard Deviation

Formulas

Standard deviation of sampling distribution formula: σ̂p = √(p(1-p)/n)

Theorems

Central Limit Theorem

Suitable Grade Level

College/University Level (Statistics)