Question

Suppose a survey of 600 young adults age 18 to 24 showed that 162 had used online dating. Calculate and interpret a confidence interval estimate for the true proportion of all young adults age 18 to 24 who ever used online dating. Use a 95% confidence level.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 162 / 600 = 0.27

1 - = 1 - 0.27 = 0.73

Z/2 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.27 * 0.73) / 600)

= 0.036

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.27 - 0.036 < p < 0.27 + 0.036

0.234 < p < 0.306

The 95% confidence interval for the population proportion p is : 0.234 , 0.306