Question

The Human Toxome Project (HTP) is working to understand the scope of industrial pollution in the human body. Industrial chemicals may enter the body through pollution or as ingredients in consumer products.

In October 2008, the scientists at HTP tested core blood samples for 35 newborn infants in the United States. The cord blood of the "In utero/newborn" group was tested for 430 industrial compounds, pollutants, and other chemicals, including chemicals linked to brain and nervous system toxicity, immune system toxicity, and reproductive toxicity, and fertility problems. There are health concerns about the effects of some chemicals on the brain and nervous system. Upon calculation of the sample, the mean of the amount of the chemical found in the infant's blood is equal to with sample standard deviation equal to.

Construct the 90% confidence interval by

- Clearly explain what model was used and why

- Clearly show your process, if using calculator explain what you did.

- Explain the meaning of the 90% confidence interval in the context of the problem.

Answer 1

Solution :

Given that,

n = 430

x = 35

Point estimate = sample proportion = = x / n = 35/430 = 0.081

1 - = 1 -0.081 = 0.919

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z0.05 = 1.645

Z/2 = 1.645

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

= 1.645 * ((0.081*(0.919) /430 )

= 0.022

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.081 -0.022 < p < 0.081 + 0.022

0.060 < p < 0.103  

(0.060 ,0.103   )