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

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

**Answer:**0.75, 0.03Find the sample proportion,

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

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):

where

is the sample proportion and

*n*is the sample size:So the standard error for the sample proportion in this example is 0.03.

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**: 0.06Use the formula for finding the margin of error (MOE):

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:

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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