Question

The Kennel Club wants to estimate the proportion of children that have a dog as a pet. Assume a 95% level of confidence and that the club estimates that 30% of the children have a dog as a pet. If the club wants the estimate to be within 3% of the population proportion, how many children would they need to contact?

Answer 1

First, we know that the level of confidence is 95%, thus we need to find the z-score associated with this level of confidence. We note that the z-score associated with a 95% confidence level is 1.96.

Then, since we already estimated that the proportion of children who own a dog as a pet is 30% (or 0.3), we will use this value as our estimated proportion. The desired margin of error is 3% (or 0.03).

The formula to calculate the necessary sample size is as follows:
(n = (z^2 * p * q) / e^2)
where:
n = sample size
z = z-score
p = estimated proportion
q = 1 - p
e = desired margin of error

Substituting the given values in the formula:
(n = (1.96^2 * 0.3 * (1 - 0.3)) / (0.03^2)
When calculated, this gives approximately 896.33.

However, since we cannot approach a fraction of a person for the survey, we will need to round up to the next whole number to ensure our sample size is large enough for our desired accuracy. Therefore, we need to survey at least 897 children.

In conclusion, to estimate the proportion of children who own a dog within a 3% margin of error and a 95% confidence level, we would need to survey a minimum of 897 children.