Question

In the US, 77% of all teens have a TV in their bedrooms, while 59% of all teens in Spain have them. A simple random sample of 500 teens from the US and 300 from Spain are selected and all are asked whether they have a TV in their bedrooms. Let p hat subscript 1 minus p hat subscript 2 be the difference in the sample proportions of teens with a TV in their bedrooms, where p hat subscript 1 is the sample proportion of US teens with a TV in their bedrooms and p hat subscript 2 is the sample proportion of Spanish teens with a TV in their bedrooms. The standard deviation of the sampling distribution of the difference in sample proportions is 0.034.

Answer 1

The margin of error for the difference in sample proportions is approximately 0.068.

Step-by-step explanation:

The margin of error for the difference in sample proportions is calculated as twice the standard deviation of the sampling distribution, considering a 95% confidence level. With a standard deviation of 0.034, doubling this value results in an approximate margin of error of 0.068.

This means that the actual difference between the proportions of US and Spanish teens with TVs in their bedrooms is estimated to lie within 0.068 of the observed difference in the sample.

This margin of error helps to define a range within which the true difference in proportions likely falls. It's crucial when making inferences about the population based on sample data, providing a sense of the precision of the sample difference.