In some year, 21 percent of all teenagers in the U.S. had checking accounts. Your bank, TeenChex Inc., is interested in targeting teenagers who do not already have a checking account.
TeenChex selects a random sample of 1,000 teenagers. Find the interval in which the chance that teenagers in the sample will not have checking accounts is approximately 95 percent. Please round your answer to the nearest whole number.

A)764 - 790
B) 790 - 816
C) 777 - 803
D) 764 - 816
E) 790 - 803

Question

In some year, 21 percent of all teenagers in the U.S. had checking accounts. Your bank, TeenChex Inc., is interested in targeting teenagers who do not already have a checking account. ​
TeenChex selects a random sample of 1,000 teenagers. Find the interval in which the chance that teenagers in the sample will not have checking accounts is approximately 95 percent. Please round your answer to the nearest whole number.
​
A)764 - 790
B) 790 - 816
C) 777 - 803
D) 764 - 816
E) 790 - 803

Quizplus · Accepted Answer

The problem can be solved using the concept of confidence intervals for proportions. Given that 21% of teenagers have checking accounts, it means 79% do not have checking accounts. For a 95% confidence interval, the formula involves the sample proportion (p), the z-value for 95% confidence (approximately 1.96 for a two-tailed test), and the sample size (n). The formula for the margin of error (E) is E = z * sqrt[(p(1-p))/n]. Substituting the given values, we find the margin of error and then apply it to the proportion of teenagers without checking accounts (0.79 * 1000) to find the interval. The interval that encompasses the range from approximately 764 to 816 is the correct answer, allowing for the variability expected in a sample of 1000 teenagers.

In Some Year, 21 Percent of All Teenagers in the U.S