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In: Statistics and Probability

Proportion Problem. Each year Delta Dental does a survey of parents concerning the tradition of the...

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.

.5 is contained in your confidence interval. This is a true or false question

Solutions

Expert Solution

Solution :

Given that,

n = 1058

x = 508

Point estimate = sample proportion = = x / n = 508/1058=0.48

1 - = 1 - 0.48=0.52

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 (((0.48*0.52) / 1058)

= 0.0396

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.48 - 0.0396< p <0.48 + 0.0396

0.4404< p < 0.5196

The 99% confidence interval for the population proportion p is : (0.4404 , 0.5196)

orchestra answered 1 year ago
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