A simple random sample of size n is drawn from a population that is normally distributed. Thesample mean, x is found to be 35.1, and the sample standard deviation, s, is found to be 8.7.NOTE: Use your calculator to find the confidence intervals and round your answer to threedecimal places.(a) Construct a 90% confidence interval for u if the sample size, n, is 40.Answer: ((b) Construct a 90% confidence interval for u if the sample size, n, is 100.Answer: (How does increasing the sample size affect the margin of error, E?Answer: Increasing the sample size(c) Construct a 98% confidence interval for u if the sample size, n, is 40.Answer: ((increases, decreases) the margin of error.Compare the results to those obtained in part (a). How does increasing the level of confidenceaffect the margin of error, E?Answer: Increasing the level of confidenceerror.(increases, decreases) the margin of

Sample mean Sample standard deviation

Answered: A simple random sample of size n is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately σ=26.1. We would like to be 99% confident that the estimate is within 3 of the true population mean. How large of a sample size is required?
Suppose you take a random sample of n = 80 Douglas College students and ask each student their age. You find that the mean age of students in this sample is X = 22.0375 years and the sample standard deviation is s = 3.2014 years. Fill in the blanks (rounding to four decimal places): The 95% confidence interval for the mean age μ of all Douglas College students is from ______ years to ______ years.
you measure the weights of a random sample of twenty-five people. The sample mean is 60 kg. Suppose that the mean weights of people follow a normal distribution with an unknown mean and standard deviation of 5 kg. You compute a 95% confidence interval for μ. The 95% confidence interval for μ is?
Let X de a normally distributed variable with a population standard deviation = 43. A research believe that the standard deviation should increase when a new variable is manipulated. To test their claim, the research collects a sample of size n = 19 and finds a sample statistic of 8 = 53. Use the x²-table to find the largest value that the corresponding P-value can be. Type your answer...
Tina catches a 14-pound bass. She does not know the population mean or standard deviation. So she takes a sample of five friends and they say the last bass they caught was 9, 12, 13, 10, and 10 pounds. Find the t and calculate a 95% (α = .05) confidence interval.
A professor was curious about her students' grade point averages. She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor's students?
The random sample of n=75�=75 yielded a sample mean of x¯=26�¯=26.Assume that we know the population standard deviation is σ=30�=30. Step 2 of 3 : Calculate a 95% confidence interval for the population mean. Round your answers to 2 decimals places.
Determine if the following statements are true or false. a. Jane took a sample of n = 100 observations from a population with mean and standard deviation. Mike also took a sample of n = 200 observations from the same population. Then, Mike’s sample mean will be closer to the true population mean than Jane’s sample. b. Jane took a sample of n = 100 observations from a population with mean and standard deviation. Mike also took a sample of n = 200 observations from a population with mean and standard deviation 2. Then, the sample mean from Mike’s sample is more likely to be close to the true mean than the sample mean from Jane’s sample. That is, the probability that X is between 90% and 110% of mean is higher for Mike’s sample than for Jane’s sample.
You would like to construct a 99% confidence interval to estimate today's population mean temperature, so you make a series of measurements (a random sample) throughout the day. The mean of these measurements is 58.5 degrees Fahrenheit, and their standard deviation is 3.0 degrees Fahrenheit. For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)

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