Questions: Assume that a sample is used to estimate a population proportion μ. Find the margin of error M.E. that corresponds to a sample of size 57 with a mean of 82.9 and a standard deviation of 19.8 at a confidence level of 99.9%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Assume that a sample is used to estimate a population proportion μ. Find the margin of error M.E. that corresponds to a sample of size 57 with a mean of 82.9 and a standard deviation of 19.8 at a confidence level of 99.9%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
Transcript text: Assume that a sample is used to estimate a population proportion $\mu$. Find the margin of error M.E. that corresponds to a sample of size 57 with a mean of 82.9 and a standard deviation of 19.8 at a confidence level of 99.9\%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = $\square$ Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
failed

Solution

failed
failed

Solution Steps

Step 1: Determine the Z-Score

For a confidence level of \(99.9\%\), the corresponding Z-score is calculated to be \(Z = 3.3\).

Step 2: Calculate the Margin of Error

The formula for the margin of error (M.E.) is given by:

\[ \text{Margin of Error} = \frac{Z \times \sigma}{\sqrt{n}} \]

Substituting the known values:

  • \(Z = 3.3\)
  • \(\sigma = 19.8\)
  • \(n = 57\)

We can express the calculation as follows:

\[ \text{Margin of Error} = \frac{3.3 \times 19.8}{\sqrt{57}} \]

Step 3: Compute the Margin of Error

Calculating the above expression yields:

\[ \text{Margin of Error} \approx 8.6 \]

Final Answer

The margin of error (M.E.) is

\[ \boxed{8.6} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
For samples of the specified size from the population described, find the mean and standard deviation of the sample mean x. One barge from Inland Waterways, Inc. can carry a load of 6284.8 lb. Records of past trips show that the weights of the cans that it carries have a mean of 94 lb and a standard deviation of 16 lb. For samples of size 64, find the mean and standard deviation of x̄.
failedAnswered
Thrombocytes are red blood cells. eosinophils. platelets. monocytes. basophils.
failedAnswered
A college education creates positive externalities. Use the accompanying graph which represents the hypothetical market for a college education in the land of Smartypants to answer the questions that follow. MSB stands for marginal social benefit, MPB stands for marginal private benefit, and MPC stands for marginal private cost. 1. Move point E to the efficient equilibrium outcome. 2. If the government of Smartypants wanted to subsidize college education, how much would it subsidize each student to achieve the socially optimal level of education?
failedAnswered
Question You are creating a custom object called "Tasks". The "Tasks" object has several fields, including Task Name, Due Date, and Priority. Which of the following options should you use to retrieve specific records from the "Tasks" object when it contains a large number of records? Select only one answer Use indexing to optimize the performance of the query. Use SOQL to query all of the records in the "Tasks" object and filter the results based on specific criteria. Use the trigger.newMap collection to retrieve the necessary records. Use a scheduled batch job to process the records in batches.
failedAnswered
System A -x+4 y = -8 x = 8+4 y The system has no solution. The system has a unique solution: (x, y)= The system has infinitely many solutions. They must satisfy the following equation: y=