Connecting a Population Proportion to a Survey

By Consumer Dummies

In the following practice problems, you will be connecting a population proportion to a survey. A website ran a random survey of 200 customers who purchased products online in the past 12 months. The survey found that 150 customers were “very satisfied.”

Sample questions

  1. What are the sample proportion and the standard error for the sample proportion, based on this data?

    Answer: 0.75, 0.03

    Find the sample proportion,

    image0.jpg

    by dividing the number of “successes” (75 in this case) by the sample size (200):

    image1.jpg

    The sample proportion represents the proportion of customers in the sample who are satisfied with their online purchases.

    Then use the following formula to find the standard error (SE):

    image2.jpg

    where

    image3.jpg

    is the sample proportion and n is the sample size:

    image4.jpg

    So the standard error for the sample proportion in this example is 0.03.

  2. With a 95% confidence level, what is the margin of error for the estimate of the proportion of all customers who purchased products online in the past 12 months?

    Answer: 0.06

    Use the formula for finding the margin of error (MOE):

    image5.jpg
    image6.jpg

    is the sample proportion, n is the sample size, and z* is the appropriate value from the standard normal distribution for your desired confidence level. For a 95% confidence level, the z*-value is 1.96. Note that the margin of error is the z*-value times the standard error.

    Now, plug in the known values and solve:

    image7.jpg

    With 95% confidence, the margin of error is plus/minus 0.06 for estimating the proportion of all customers who purchased products online in the past 12 months.

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