**Title: Calculating Minimum Sample Size for a 90% Confidence Level****Introduction:**When conducting statistical analysis, determining the appropriate sample size is crucial to ensure the reliability of the results. Below is an explanation of how to calculate the minimum sample size required to be 90% confident that the sample mean is within one unit of the population mean, given a standard deviation \( \sigma = 11.3 \). The assumption is that the population is normally distributed.**Problem Statement:**Determine the minimum sample size required for a 90% confidence level given:- Desired margin of error (E) = 1 unit- Population standard deviation (\( \sigma \)) = 11.3**Calculation:**1. **Z-Score for 90% Confidence Level:** - The Z-score associated with a 90% confidence level can be found in statistical Z-tables or using a standard normal distribution calculator. It is approximately 1.645.2. **Formula for Sample Size (n):** \[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \] - Where \( n \) is the sample size, - \( Z \) is the Z-score (1.645 for 90% confidence), - \( \sigma \) is the population standard deviation (11.3), - \( E \) is the margin of error (1 unit).3. **Plug in the Values:** \[ n = \left( \frac{1.645 \cdot 11.3}{1} \right)^2 \] \[ n = \left( 18.5885 \right)^2 \] \[ n \approx 345.64 \]4. **Rounding:** - Round up to the nearest whole number to ensure the sample size is sufficient. - Therefore, the minimum sample size required is 346.**Conclusion:**For a 90% confidence level with a margin of error of 1 unit, you should use a sample size of approximately 346 to ensure accuracy, assuming the population is normally distributed.

Determine the minimum sample size required when you want to be 90% confident that the sample mean is within one unit of the population mean and o = 11.3. Assume the population is normally distributed. A 90% confidence level requires a sample size of: (Round up to the nearest whole number as needed.)

Determine the minimum sample size required when you want to be 90% confident that the sample mean is within one unit of the population mean and o = 11.3. Assume the population is normally distributed. A 90% confidence level requires a sample size of: (Round up to the nearest whole number as needed.)

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

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.
Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ=19.5. Assume the population is normally distributed. Question content area bottom Part 1 A 99% confidence level requires a sample size of enter your response here . (Round up to the nearest whole number as needed.)
Use the given to find the minimum sample size required to estimate a population proportion or percentage. Margin of error :0.09, confidence level 95%; p and Q unknown
If X=101, o=27, and n= 32, construct a 95% confidence interval estimate of the population mean, p
may i know the answer??????????
Determine the minimum sample size required when you want to be 95% confident that the sample mean is within two units of the population mean and = 4.3. Assume the population is normally distributed. n =
With 99% confidence, maximum error is 0.06 and the proportion p = 0.5. Find the sample size. a. 463 b. 436 c. 364 d. 643 e. NONE OF THE ABOVE A
Using the given margin of error, confidence level, and likely range for the observed value of the sample proportion, obtain a sample size that will ensure a margin of error of at most the one specified (provided, of course, that the observed value of the sample proportion is further from 0.5 than the educated guess). margin of error = 0.01; confidence level = 95%; likely range = 0.3 to 0.4 The required sample size is n = (Round up to the nearest whole number.)
Researchers studied the mean egg length (in millimeters) for a bird population. After taking a random sample of eggs, they obtained a 95% confidence interval of (45,60). What is the value of the margin of error? Choose the correct answer below. A. 15 mm B. 52.5 mm O c. 7.5 mm O D. 1.96
Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 272 with 27.9% successes at a confidence level of 80%. M.E. = % Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. Round final answer to one decimal place Question Help: Video Submit Question MacBook Air 80 888 F5 F6 F7 F8 F1 F2 F3 F4 @ # & 2 3 6. 7 8 W Y S D H. J K C V S LO R
Use the given data to find the 95% confidence interval estimate of the population mean . Assume that the population has a normal distribution. IQ scores of professional athletes: Sample size n = 10 Mean 106 Standard deviations = O