Question

In a sample of 200 homes in Lagrange, 40 were found to have unsafe radon levels...

In a sample of 200 homes in Lagrange, 40 were found to have unsafe radon levels and of 100 homes in Hyde Park, 30 had unsafe radon levels. Form a 95% confidence interval on the difference in the proportions.

Homework Answers

Answer #1

Answer:

Given,

n1 = 200

n2 = 100

X1 = 40

X2 = 30

p1 = X1/n1

p1 = 40/200

p1 = 0.2

p2 = X2/n2

p2 = 30/100

p2 = 0.3

p bar = (n1p1 + n2p2)/(n1 + n2)

p bar = (200*0.2 + 100*0.3)/(200+100)

p bar = 0.2333

q bar = 1 - pbar

= 1 - 0.233

q bar = 0.77

SE(p1 -p2) = sqrt((pbar*q bar (1/n1)+(1/n2)))

substitute values in above expression

SE(p1 - p2) = sqrt(0.2333*0.77*((1/200)+(1/100)))

= sqrt(2.69115*10^-3)

SE(p1 - p2) = 0.052

consider,

1-alpha = 0.95

alpha = 0.05

alpha/2 = 0.025

Zalpha/2 = Z0.025 = 1.96 [since from the standard normal distribution table]

Interval can be given as follows

(p1 - p2) +/- Zalpha/2 SE(p1-p2)

substitute values

= (0.2-0.3) +/- 1.96(0.052)

= (- 0.20192 , 0.00192)

Hence the 95% confidence interval for (p1 - p2)difference are (-0.20192 , 0.00192)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
When Abraham Lincoln was first elected to the presidency, he received 39.82% of the 1,865,908 votes...
When Abraham Lincoln was first elected to the presidency, he received 39.82% of the 1,865,908 votes cast. The collection of all of those votes is the population being considered. Is the 39.82% a parameter or a statistic? Part (a) gives the total votes cast in the 1860 presidential election. Consider the total numbers of votes cast in all presidential elections. Are those values discrete or continuous? c. How many votes did Lincoln get when he was first elected to the...
A random sample of 200 apples was taken from an orchard and 30 were found rotten....
A random sample of 200 apples was taken from an orchard and 30 were found rotten. Form a 99% confidence interval for the proportion of rotten apples in the orchard
Data was gathered about vaccination rates in small nursing homes (group 1) and large nursing homes...
Data was gathered about vaccination rates in small nursing homes (group 1) and large nursing homes (group 2) and those that had below 80% of their residents vaccinated were flagged for audit. Based on the number of those that had a low vaccination rate, the following confidence interval for the difference of proportions was created: -.1877 < p1 −p2 <-.1103 a) What can be concluded about the populations based on this interval? b) What is the margin of error in...
In a sample of 200 people, it was found that they spend a mean of $250...
In a sample of 200 people, it was found that they spend a mean of $250 per month on cable and internet, with a standard deviation of $30. Compute a 95% confidence interval for the population mean and population standard deviation.
In a sample of 100 women, 30 percent had a college degree, while in a sample...
In a sample of 100 women, 30 percent had a college degree, while in a sample of 100 men, 25 percent had a college degree. (a) Find a 95 percent confidence interval for the population proportion of women having a college degree. (b) Find a 95 percent confidence interval for the population proportion of men having a college degree. (c) Find a 95 percent confidence interval for the difference in population proportions of women and men having college degrees.
From a random sample of 780 US homes it was found that 655 had broadband Internet...
From a random sample of 780 US homes it was found that 655 had broadband Internet access. Construct a 99% confidence interval for the proportion of US homes with broadband Internet access. Interpret your result.
Most musicians have different popularities among various age groupings. In a random sample of 200 high...
Most musicians have different popularities among various age groupings. In a random sample of 200 high school students, 163 said they liked Beyoncé or her work. In a random sampling of 200 adults aged 30 to 40, 128 of them said they liked Beyoncé or her work. Write down the formula needed in order to create a 95% confidence interval: Construct a 95% confidence interval for the difference in the proportion of students that like Beyonce or her work and...
A random sample of 732 judges found that 405 were introverts. a. Construct a 95% confidence...
A random sample of 732 judges found that 405 were introverts. a. Construct a 95% confidence interval for the proportion. b. Interpret the meaning of the confidence interval. Justify your use of a confidence interval based on a normal distribution for data regarding proportions that are normally following a binomial distribution. Note: Please show detailed working and justification.
Many homeowners buy detectors to check for the invisible gas radon in their homes. We want...
Many homeowners buy detectors to check for the invisible gas radon in their homes. We want to determine the accuracy of these detectors. To answer this question, university researchers place 12 radon detectors in a chamber that exposed them to 105 picocuries per liter of radon. The detector readings were as follow: 91.9 97.8 111.4 122.3 105.4 95.0 103.8 99.6 96.6 119.3 104.8 101.7 Assume that σ = 9 picocuries per liter of radon for the population of all radon...
When conducting sequential sampling in simulation output analysis of 40 replications, the sample mean is found...
When conducting sequential sampling in simulation output analysis of 40 replications, the sample mean is found to be 3.20, and the sample variance is found to be 0.25. a) Calculate the 95% confidence interval. b) Explain how to reduce the half width by 50%. c) Explain the difference between relative and absolute precision as it applies to this example.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT