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The proportion of drivers who use seat belts depends on things like age, sex, and ethnicity....

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 _

Expert Solution

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} * $\sqrt$ (( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((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)

milcah answered 2 months ago

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