Question

Question 31 3 pts Proportion Problem. Each year Delta Dental does a survey of parents concerning the tradition of the Tooth Fairy. A random sample of 1,058 parents were asked about how much money they leave for a tooth and questions concerning how their child responded to the concept of the Tooth Fairy. In one question, 508 parents indicated that their child saved the money they got for their tooth. You are asked to calculate a 99% Confidence Interval for this proportion. What is the Lower Value in this Confidence Interval? I just want the answer. Use 4 decimal places for your answer and use the proper rules of rounding.

Answer 1

Solution :

Given that,

n = 1058

x = 508

Point estimate = sample proportion = $\hat p$ = x / n = 508 /1058=0.480

1 - $\hat p$ = 1 - 0.480=0.520

At 99% confidence level the z is ,

$\alpha$  = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ =0.01

Z_$\alpha$ = Z_0.01 = 2.326

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$ (($\hat p$ * (1 - $\hat p$ )) / n)

= 2.326 ($\sqrt$((0.480*0.520) /1058 )

= 0.0357

A 99% confidence interval for population proportion p is ,

$\hat p$ - E

0.480 - 0.0357

=0.4443

lower value = 0.4443