# Question: The large sample confidence interval for a proportion substitutes p for

The large-sample confidence interval for a proportion substitutes p̂ for the unknown value of p in the exact standard error of p̂. A less approximate 95% confidence interval has endpoints determined by the p values that are 1.96 standard errors from the sample proportion, without estimating the standard error. To do this, you solve for p in the equation

| p̂ - p | = 1.961√p(1 - p)/n.

a. For Example 11 with no students without iPods in a sample of size 20, substitute pn and n in this equation and show that the equation is satisfied at p = 0.83337 and at p = 1. So the confidence interval is (0.83887, 1), compared to (1, 1) with p̂ ± 1.96(se).

b. Which confidence interval seems more believable? Why?

| p̂ - p | = 1.961√p(1 - p)/n.

a. For Example 11 with no students without iPods in a sample of size 20, substitute pn and n in this equation and show that the equation is satisfied at p = 0.83337 and at p = 1. So the confidence interval is (0.83887, 1), compared to (1, 1) with p̂ ± 1.96(se).

b. Which confidence interval seems more believable? Why?

**View Solution:**## Answer to relevant Questions

When the population distribution is normal, the population mean equals the population median. How good is the sample median as a point estimate of this common value? For a random sample, the estimated standard error of the ...Refer to the previous exercise. Show how you can get a 95% confidence interval for the proportion of American adults who were opposed to the death penalty from the confidence interval stated in the previous exercise for the ...Using the Confidence Interval for a Proportion applet on the text CD, let’s check that the large-sample confidence interval for a proportion may work poorly with small samples. Set n = 10 and p = 0.10. Generate 100 random ...For the question about e-mail in the previous exercise, suppose seven females in the GSS sample of age at least 80 had the responses 0, 0, 1, 2, 5, 7, 14, a. Using software or a calculator, find the sample mean and standard ...A company that sells its products through mail-order catalogs wants information about the success of its most recent catalog. The company decides to estimate the mean dollar amount of items ordered from those who received ...Post your question