Question

An analyst, using a random sample of n = 500 families, obtained a 90% confidence interval for mean monthly family income for a large population: ($2700, $3300). If the analyst had sampled 1000 families instead, what would be different? The new interval from 1000 families would be narrower (shorter). The intervals would have the same width. The answer cannot be determined from the information given. The new interval from 1000 families would be wider (longer). We cannot say because the condition for randomness, independence, or normality is not met.

Answer 1

Increasing the sample size causes the confidence interval to be wider and making the margin of error lower. Thus, it provides a more detailed approximate of the population. So the answer is that the new interval from 1000 families would be making the interval narrower.