A study was conducted to determine the percent of children that want to grow up work in the same career as a parent. In a sample of 200 children, it was calculated that 43% wanted to eventually work in the same career as a parent. Construct the 95% confidence interval for the population proportion. Solution: phat = 0.43/200 = 0.00215 phat - qnorm (1.95/2) * sqrt (phat * (1-phat) / 200) = - 0.00426926 phat + qnorm (1.95/2) * sqrt (phat * (1-phat) / 200) = 0.00856926 [-0.0043, 0.0086] What is wrong with this solution?

Question

Mathematics

Juan Mann

2 November, 20:48

A study was conducted to determine the percent of children that want to grow up work in the same career as a parent. In a sample of 200 children, it was calculated that 43% wanted to eventually work in the same career as a parent. Construct the 95% confidence interval for the population proportion. Solution: phat = 0.43/200 = 0.00215 phat - qnorm (1.95/2) * sqrt (phat * (1-phat) / 200) = - 0.00426926 phat + qnorm (1.95/2) * sqrt (phat * (1-phat) / 200) = 0.00856926 [-0.0043, 0.0086] What is wrong with this solution?

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Answers (1)

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Davenport · Answer 1

Step-by-step explanation:

From the information given,

Number of sample, n = 200

Probability of success, p = 43/100 = 0.43

q = 1 - p = 1 - 0.43

q = 0.57

For a confidence level of 95%, the corresponding z value is 1.96.

The formula for determining the error bound for the proportion is

z * √pq/n

= 1.96 * √ (0.43 * 0.57) / 200

= 1.96 * 0.035 = 0.0686

The upper boundary of the population proportion is

0.43 + 0.0686 = 0.5

The lower boundary of the population proportion is

0.43 - 0.0686 = 0.4

The error in the solution is

phat = 0.43/200 = 0.00215

Also,

[-0.0043, 0.0086] is wrong