SOLUTION: You measure 22 backpacks' weights, and find they have a mean weight of 47 ounces. Assume the population standard deviation is 10.9 ounces. Based on this, what is the maximal margin

Question 1199868: You measure 22 backpacks' weights, and find they have a mean weight of 47 ounces. Assume the population standard deviation is 10.9 ounces. Based on this, what is the maximal margin of error associated with a 95% confidence interval for the true population mean backpack weight.
Give your answer as a decimal, to two places

Answer by ElectricPavlov(122) (Show Source): You can put this solution on YOUR website!
**1. Find the Critical Value (z*)**
* For a 95% confidence level, the critical value (z*) is 1.96. This value corresponds to the z-score that captures 95% of the data within two standard deviations of the mean in a standard normal distribution.
**2. Calculate the Standard Error**
* Standard Error (SE) = σ / √n
* where:
* σ = population standard deviation (10.9 ounces)
* n = sample size (22 backpacks)
* SE = 10.9 / √22
* SE ≈ 2.32 ounces
**3. Calculate the Margin of Error**
* Margin of Error = z* * SE
* Margin of Error = 1.96 * 2.32
* Margin of Error ≈ 4.54
**Therefore, the maximal margin of error associated with a 95% confidence interval for the true population mean backpack weight is approximately 4.54 ounces.**

RELATED QUESTIONS
You measure 21 backpacks' weights, and find they have a mean weight of 45 ounces. Assume... (answered by Theo)

You measure 45 backpacks' weights, and find they have a mean weight of 49 ounces. Assume... (answered by Theo)

You measure 47 textbooks' weights, and find they have a mean weight of 59 ounces. Assume... (answered by Boreal)

You measure 22 textbooks' weights, and find they have a mean weight of 73 ounces. Assume... (answered by ewatrrr)

You measure 41 textbooks' weights, and find they have a mean weight of 49 ounces. Assume... (answered by robertb)

You measure 34 watermelons weights, and find they have a mean weight of 59 ounces.... (answered by Boreal)

#1 You measure 28 textbooks' weights, and find they have a mean weight of 41 ounces.... (answered by Boreal)

You measure 45 textbooks' weights, and find they have a mean weight of 40 ounces. Assume... (answered by oscargut)

You measure 30 textbooks' weights, and find they have a mean weight of 78 ounces. Assume... (answered by math_tutor2020)