# Inferential Statistics/ Please explain how this is done

**Question description**

- In previous problems, we have been concerned with
finding a 95% confidence interval for a population proportion. Although a
95% confidence interval is most common (public opinion polls use it almost
exclusively), other confidence intervals are easy to define and calculate.
We know that a 95% confidence interval contains the values that are within
2 standard errors of the sample proportion because the distribution of
sample proportions is assumed to be normal, and 95% of the sample
proportions are within 2 standard errors (standard deviations) of the
population proportion. Similarly, we can define a 99.7% confidence
interval, which would be based on 3 standard errors, since 99.7% of all
sample proportions are within 3 standard errors of the population
proportion. Other commonly used confidence intervals are a 99% confidence
interval based on 2.58 standard errors and a 90% confidence interval based
on 1.65 standard errors.

In some opinion poll, out of a sample of 1,370 adults nationwide, 42% supported a complete ban on all research into human cloning, without exception.

Find a 90% confidence interval for the proportion of adults who support a complete ban on all research into human cloning. Please round the answers to the nearest tenth.

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