Question

The proportion of drivers who use seat belts depends on things like age, sex, and ethnicity. As part of a broader study, investigators observed a random sample of 123 female Hispanic drivers in Boston. 68 of those in the sample were observed wearing a seat belt. Find the 95% confidence interval (±0.0001) for the proportion of all female Hispanic drivers in the Boston area who wear seat belts. The 95% confidence interval is from _ to _

Answer 1

Solution :

Given that,

n = 123

x = 68

Point estimate = sample proportion = = x / n = 68 / 123=0.553

1 - = 1 - 0.553=0.447

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 (((0.553*0.447) /123 )

= 0.0879

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.553 - 0.0879< p <0.553 + 0.0879

0.4651< p < 0.6409

The 95% confidence interval for the population proportion p is :(0.4651 TO   0.6409)