Final answer:
To calculate the critical value for an 80% confidence interval for the population proportion, one must look for the Z score corresponding to the 90th percentile of a standard normal distribution, resulting in a critical value of approximately 1.28.
Step-by-step explanation:
The critical value for an 80% confidence interval for the population proportion can be found using a standard normal (Z) distribution, as confidence intervals for proportions typically assume that the sampled proportion is close enough to the population proportion for the binomial distribution to be approximated by the normal distribution. For an 80% confidence level, we want the middle 80% of the distribution, so we exclude 20% from the tails (10% from each tail). To find this critical value, we typically would use a Z-table, statistical software, or calculator to determine the Z score that corresponds to the upper 90th percentile (since 10% is in the upper tail).
For an 80% confidence interval, the critical value (Z score) is approximately 1.28. This means that we would expect the population proportion to lie within 1.28 standard errors of the sample proportion, in the middle 80% of the distribution.