Question

A market researcher for a provider of ipod accessories wants to know the proportion of customers who own cars to access the market for a new ipod car charger. A survey of 500 customers indicates that 76% own cars. How large would the standard deviation have to be if he had surveyed only 125 customers assuming the proportion is about the same?

Answer 1

The standard deviation would have to be approximately 0.1731 if the market researcher surveyed only 125 customers assuming the proportion is about the same.

Step-by-step explanation:

To find out how large the standard deviation would have to be if the market researcher surveyed only 125 customers, we can use the formula for the standard error of a proportion:

SE = sqrt((p * (1 - p)) / n)

Where:

• SE is the standard error
• p is the proportion of customers who own cars (0.76)
• n is the sample size (500)

Substituting the given values into the formula, we get:

SE = sqrt((0.76 * (1 - 0.76)) / 500) = 0.01953

Since the standard deviation is equal to the standard error multiplied by the square root of the sample size, we can calculate the standard deviation for the sample size of 125:

SD = SE * sqrt(n) = 0.01953 * sqrt(125) = 0.1731

Therefore, the standard deviation would have to be approximately 0.1731 if the market researcher surveyed only 125 customers assuming the proportion is about the same.