### Confidence Intervals and Sample SizeThe mean and standard deviation of a random sample of \( n \) measurements are equal to 34.9 and 3.7, respectively.**a. Find a 99% confidence interval for \( \mu \) if \( n = 121 \).****b. Find a 99% confidence interval for \( \mu \) if \( n = 484 \).****c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?**### Explanation of Concepts#### Confidence IntervalA confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. The 99% confidence interval means we are 99% certain that the true population mean lies within this interval.#### Effect of Sample SizeIncreasing the sample size generally results in a narrower confidence interval, assuming the level of confidence remains the same. This is because larger samples tend to give more reliable estimates of the population parameter.### Detailed Steps to Solve1. **Identify the given values:** - Sample mean (\( \bar{x} \)) = 34.9 - Standard deviation (\( s \)) = 3.72. **Determine the confidence level:** - 99% confidence level3. **Find the critical value (\( Z_{\alpha/2} \)) corresponding to the 99% confidence level using standard normal (Z) distribution.**4. **Calculate the standard error of the mean:** \[ SE = \frac{s}{\sqrt{n}} \]5. **Determine the margin of error:** \[ Margin\ of\ Error = Z_{\alpha/2} \times SE \]6. **Construct the confidence interval:** \[ CI = \bar{x} \pm Margin\ of\ Error \]#### For part a: \( n = 121 \)#### For part b: \( n = 484 \)#### For part c: Compare the widths of the intervals found in parts a and b. Analyze the effect of increasing the sample size.By following these steps and calculations, you can understand how sample size affects the width of the confidence interval while maintaining the same confidence

Given information Sample mean, x-bar = 34.9 Population standard deviation, σ = 3.7 Since population…

The mean and standard deviation of a random sample of n measurements are equal to 34.9 and 3.7, respectively. a. Find a 99% confidence interval for u if n = 121. b. Find a 99% confidence interval for u ifn=484. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

The mean and standard deviation of a random sample of n measurements are equal to 34.9 and 3.7, respectively. a. Find a 99% confidence interval for u if n = 121. b. Find a 99% confidence interval for u ifn=484. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

a hamburger chain sells hamburger. A random sample of 25 hamburger is taken and each is weighed. the mean of this sample is 0.26 pound and the standard deviation of 0.03 pound. Suppose you you were asked to find the 95% confidence interval. what MARGIN of error should you use? Use the multiplier t*= 2.064 to calculate and round your answer to the three decimal places A. 0.061 B. 0.006 C. 0.107 D. 0.012
Let n1=100, X1=60, n2=100, and X2=80. a. Determine the zstat, based on the difference p1−p2, and the p-value. b.Determine a conclusion c. Construct a 95% confidence interval estimate of the difference between the two population proportions.
A random sample of 88 observations produced a mean x=25.8 and a standard deviation s=2.5. a. Find a 95% confidence interval for μ. b. Find a 90% confidence interval for μ. c. Find a 99% confidence interval for μ. a. The 95% confidence interval is (enter your response here,enter your response here).
Construct the confidence interval for the population mean μ. c= 0.90, x= 9.1, o = 0.4, and n = 60 A 90% confidence interval for u is (Round to two decimal places as needed.)
Construct the confidence interval for the population mean u. c=0.98, x=16.5, o=4.0, and n=60. A 98% confidence interval for u is (___,___). (Round to one decimal place as needed.
I have only 30 min. Please help
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 80% confidence interval with an error of no more than 0.07 . A consultant has informed them that a previous study found the mean to be 3.6 energy drinks per week and found the variance to be 1.44 . What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
Construct the confidence interval for the population mean μ. c= 0.90, x= 16.7, o = 2.0, and n = 60 A 90% confidence interval for u is . (Round to one decimal place as needed.)
At a charter high school, the average GPA of a high school senior is known to be normally distributed. After a sample of 27 seniors is taken, the average GPA is found to be 2.85 and the sample variance is determined to be 0.16. Find a 95% confidence interval for the population mean GPA. a. 2.5615 to 2.8585 b. 2.6358 to 3.0642 c. 2.6917 to 3.0083 d. 2.5167 to 2.9033
Construct a 99% confidence interval for u, - H, with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances Stats X, = 98 mg, s,= 3.81 mg, n, = 14 x = 65 mg, s, =222 mg, n, =20 Confidence interval when variances are not equal +t. n2 d.f. is the smaller of n, - 1 or n, - 1 Enter the endpoints of the interval